Sparkler Chemistry: Why a Molten Iron Droplet Bursts Into Branches

What Is Actually Painted on the Wire

A sparkler is not a flame on a stick but a slow solid-propellant charge on a steel wire 0.8–1 mm thick and 18–90 cm long. A representative mix is ~50% barium nitrate, ~32% iron or steel powder, ~10% dextrin, a few percent aluminium and 0.1–2% boric acid, slurried with water, dipped and dried.

• Ba(NO₃)₂ is the oxygen tank. It melts at 592 °C and decomposes: Ba(NO₃)₂ → BaO + N₂ + 2.5 O₂. That 2.5 mol of O₂ is 80.0 g out of a formula mass of 261.3 g/mol, so the salt surrenders 30.6% of its own mass as oxygen.
• Dextrin is fuel and glue. Roasted starch holds the paste on the wire, then burns in the nitrate's oxygen, driving the front at a few millimetres per second — 45–60 s for a 25 cm sparkler — at ~1,000–1,600 °C.
• Iron powder, 50–300 µm, is the passenger, there only to be released, melted and thrown.
• Aluminium adds brilliance; boric acid keeps a damp mix acidic so the aluminium cannot attack the nitrate in storage.

A budget shows why the sparks matter more than the wire. Per 100 g of paste, 50 g of Ba(NO₃)₂ is 0.191 mol and liberates 0.478 mol O₂. Burning 10 g of dextrin, (C₆H₁₀O₅)ₙ at 162 g per unit, to CO₂ and water takes 6 O₂ per unit — 0.370 mol, leaving 0.108 mol. The few percent of aluminium then claims almost all of that remainder (4 g of Al needs 0.111 mol O₂ to reach Al₂O₃), so effectively nothing is left for the 32 g (0.573 mol) of iron, which would need 0.382 mol to reach Fe₃O₄. The wire cannot oxidise most of its own iron. It leaves molten and unburnt and finds oxygen in room air — the sparks are where most of the reaction happens.

The Life of One Spark, Step by Step

1. The front arrives. Molten barium nitrate decomposes, the dextrin burns in the oxygen it releases, and gas expands violently inside a millimetre-thick shell of paste.

2. A particle is set free. One iron particle, 50–300 µm, loses its binder, heats through its ignition point near 1,030–1,130 K, and is kicked clear.

3. It melts. Pure iron melts at 1,538 °C (1,811 K), and its dissolved carbon lowers that: at 0.5 wt% C the Fe–C liquidus sits near 1,500 °C (1,770 K). Surface tension pulls the melt into a near-perfect sphere — exactly what Robert Hooke found when he caught flint-and-steel sparks on paper in 1665 and put them under a microscope.

4. It burns in the air. 3 Fe + 2 O₂ → Fe₃O₄, ΔH = −1,118 kJ/mol. The droplet self-heats to ~1,800–2,200 K, a few hundred kelvin clear of that liquidus so it stays fully liquid, and glows gold.

5. It grows a liquid skin, not a crust. At that temperature the inner, wüstite-rich sheath is molten too — FeO melts at 1,377 °C, magnetite Fe₃O₄ at 1,597 °C — so oxygen does not merely burn the surface, it dissolves inward through a mobile sheath.

6. The carbon is waiting. Steel powder carries 0.1–0.7 wt% carbon, dissolved since the day it was smelted, and oxygen arriving from outside meets it at the liquid-metal/liquid-oxide interface.

7. It bursts, and the daughters do it again. Carbon monoxide inflates, the skin ruptures, two to four daughters fly off at the fork angles you see. Each still holds carbon, so each repeats the cycle — up to four generations from one grain.

The Carbon Boil: A Reaction That Runs Uphill

The rupture step is one reaction: FeO + C → Fe + CO, ΔH ≈ +162 kJ/mol — written for species already dissolved in the melt it becomes [C] + [O] → CO(g), the brackets meaning dissolved in liquid iron. The enthalpy quoted here is for the oxide form, which is the one the droplet actually runs: the oxygen arrives as the liquid oxide skin.

Read that enthalpy again: the burst reaction is endothermic. Nothing about a hot droplet makes it happen — entropy does. A gas appears where there were only condensed phases, a standard entropy change of about +159 J/(mol·K). Setting ΔG = ΔH − TΔS to zero gives the crossover:

T ≈ 162,000 J/mol ÷ 159 J/(mol·K) ≈ 1,020 K, roughly 750 °C.

Above about 1,000 K the entropy term wins and carbon strips oxygen out of iron oxide even though it costs energy. The droplet sits at 1,800–2,200 K, about twice the crossover, so the reaction runs hard — and cools the droplet while running, which is part of why oxidation and boiling alternate rather than happening once.

The decisive fact is the product. Carbon dissolves in liquid iron. Oxygen dissolves in liquid iron. Carbon monoxide does not. Its only route out is a bubble, nucleating at the metal/oxide interface where the barrier is lowest; homogeneous nucleation in clean liquid iron would demand thousands of bar of supersaturation and essentially never happens.

This is no exotic fireworks effect. It is the carbon boil, the decarburisation stage Henry Bessemer harnessed in 1856 when he blew cold air through molten pig iron and watched the bath erupt as its carbon left as CO. A sparkler spark is a Bessemer converter a few hundred billion times smaller by mass — a ten-tonne charge of pig iron against 29 micrograms of steel.

Working the Numbers: 400 Droplet-Volumes Against 0.7 Bar

Take one typical spark: a sphere 200 µm across, so r = 1×10⁻⁴ m.

• Volume: (4/3)πr³ = 4.19×10⁻¹² m³, about 4.2 nanolitres.
• Mass: liquid iron is ~7.0 g/cm³, so m ≈ 2.9×10⁻⁵ g — 29 micrograms.
• Carbon aboard: at 0.5 wt%, 1.5×10⁻⁷ g, or n = 1.2×10⁻⁸ mol.
• Gas it makes: V = nRT/P = (1.2×10⁻⁸ × 8.314 × 1,800) ÷ 101,325 ≈ 1.8×10⁻⁹ m³ = 1.8 microlitres.

Divide: 1.8×10⁻⁹ ÷ 4.19×10⁻¹² ≈ 430. One spark's carbon can make roughly 400 times the droplet's own volume of gas — a balloon the droplet cannot possibly contain.

Only a fraction need come out at once. A bubble must beat ambient pressure plus the Laplace overpressure of the surface it pushes against, ΔP = 2σ/r. Liquid iron's surface is unusually stiff, σ ≈ 1.8 N/m, about 25 times water's. The r that matters is the bubble's, not the droplet's; take a bubble grown to r = 50 µm, half our droplet's radius:

2σ/r = (2 × 1.8) ÷ (5×10⁻⁵) = 7.2×10⁴ Pa ≈ 0.7 bar

So the bubble needs ~1.7 bar absolute before it grows freely — and past that the restoring force falls, because 2σ/r shrinks as r grows. Growth is unstable and the skin fails in a few hundred microseconds, which is why a fork is a sharp event rather than a slow bulge.

One check on the spark's whole life: oxidising 29 µg of iron to Fe₃O₄ releases 1,118 kJ per 167.5 g of Fe, or 6.7 kJ/g — about 0.19 J. A 200 µm sphere (area 1.26×10⁻⁷ m²) at 1,900 K with emissivity ~0.8 radiates εσT⁴A ≈ 0.07 W. Energy over power gives ~2.6 s — the right order for a spark you can watch cross a metre of air.

Reading Sparks as a Measurement

Because forking counts carbon, the spark is a measurement, used as one for a century. Press a sample to a grinding wheel in a darkened bay and read the stream: the spark test is codified in JIS G 0566, Method of Spark Test for Steel. Roughly, ~0.15 wt% C gives long straw streaks with rare forks; ~0.5 wt% gives repeated two- and three-way bursts; 1.0 wt% and above gives dense chrysanthemum sprays. Alloys leave fingerprints too: tungsten darkens the stream and kills the bursts, silicon suppresses them, manganese multiplies them.

In the laboratory the event is filmed directly at tens of thousands of frames per second. Peng et al., Combustion and Flame 274 (2025), resolved the micro-explosion in single iron particles carrying just 0.117 wt% carbon — a tenth of a percent is already enough. The motivation is not fireworks: iron powder is being developed as a recyclable carbon-free fuel, and micro-explosions reshape its burning particle size distribution.

Factory control is ordinary process chemistry: sieve or laser diffraction to hold the 50–300 µm iron window, TGA and DSC for where the nitrate melts and decomposes, UN Test Series friction and impact sensitivity, and a gassing test near 60 °C — the test the boric acid level is tuned against.

As a product a sparkler is a regulated article: in the EU, category F1 under Directive 2013/29/EU, minimum age 12, built to the EN 15947 series, which specifies among other things an unlit grip length. In the US it falls under the Federal Hazardous Substances Act with CPSC requirements in 16 CFR Parts 1500 and 1507, and wire sparklers carrying no more than 100 g of composition are classed as novelties rather than consumer fireworks under industry standard APA 87-1, the classification ATF and most state fire codes follow — which is why several states that ban consumer fireworks still permit them. They ship as UN 0337 (1.4S) or UN 0336 (1.4G).

How It Fails, and How People Get Hurt

The storage failure is chemical, not thermal. Aluminium plus nitrate plus moisture is a bad combination. Ba(NO₃)₂ is itself a neutral salt, but technical grades carry traces of carbonate and hydroxide, so a damp paste drifts alkaline; hydroxide strips aluminium's oxide film, and the exposed metal reduces nitrate toward ammonia while evolving hydrogen — exothermically, and the ammonia pushes the pH higher still, so the attack feeds itself. A packed box of damp sparklers can self-heat and ignite with no external flame. The 0.1–2% boric acid exists solely to buffer that mix acidic and keep the aluminium passive.

The burn is usually the wire, not the flame. After burnout the steel stays hundreds of degrees for tens of seconds while looking inert. That, plus a front at 1,000–1,600 °C — hot enough to melt gold, at 1,064 °C — is why CPSC's fireworks reports repeatedly place sparklers among the leading causes of emergency-room-treated fireworks injuries, children under five most affected.

The catastrophic misuse is bundling. Taping a hundred or more sparklers together turns a slow deflagrating novelty into a self-confining mass that can transition to an explosion. ATF and CPSC have both warned about sparkler bombs, which have caused amputations and deaths; building one is a felony in the United States.

And the residue is toxic. Soluble barium salts are potassium-channel poisons and barium nitrate's oral LD₅₀ in rats is around ~350 mg/kg, so unburnt paste is not a toy. Burnt residue is mainly BaO, which takes up atmospheric CO₂ to become the far less soluble BaCO₃ — but BaO is not itself benign: with water it gives soluble, caustic Ba(OH)₂. Sparklers at least avoid the perchlorate that contaminates water near large displays, their oxidiser being a nitrate.

The Look-Alikes It Gets Confused With

It is not a flame test. The commonest error by far. Barium is in a sparkler as an oxygen supply, not a colourant. The gold is incandescence — continuous, blackbody-like emission from ~1,800 K iron. Wien's law puts that curve's peak at 2.898×10⁻³ ÷ 1,800 ≈ 1,610 nm, deep in the infrared, so only the short-wavelength tail escapes as light, and a tail that steep reads gold-orange. A barium flame test is something else: sharp apple-green emission around 505–535 nm, which in pyrotechnics needs a chlorine donor (PVC, Parlon, hexachloroethane) to form the BaCl emitter. A sparkler has none. No chlorine, no green.

It is not magnesium or aluminium. Those give brilliant white, essentially straight sparks: no dissolved carbon, so no non-condensable gas to inflate. Aluminium can fragment when an alumina shell ruptures, but never with the generational branching of carbon-bearing iron. Pure titanium throws silver-white needles; the branching silver sparks sold in fireworks are ferro-titanium, an iron alloy, which branches for the same reason a sparkler does.

It is not thermite; it is thermite run backwards. Thermite is 3 Fe₃O₄ + 8 Al → 4 Al₂O₃ + 9 Fe, aluminium taking oxygen away from iron oxide. In a sparkler, iron is the fuel and Fe₃O₄ is the product.

It is not quite burning steel wool. Wool oxidises by the same route, but the fibres stay connected: no free droplet, no sealed oxide sheath, and gas escapes along the fibre instead of inflating a sphere — glowing and a few thrown sparks, not four generations of forks. Grinding sparks are the identical phenomenon, which is why the sparkler in a child's hand and the spark test in a steel mill are chemically one experiment.

Sparks look alike and are not alike. Only a carbon-bearing iron droplet forks, because only it makes a gas that cannot dissolve.

Spark source	What is actually burning	Colour and temperature	Does it fork?
Sparkler (barium nitrate + iron powder)	Free iron droplets oxidising in room air to Fe₃O₄	Gold-orange incandescence, ~1,800–2,200 K	Yes — 2 to 4 daughters per burst, up to 4 generations, driven by dissolved carbon
Grinding a 1.0 wt% carbon tool steel	Identical mechanism: torn-off droplets with lots of dissolved carbon	Gold-white, ~2,000 K	Yes, densely — repeated chrysanthemum bursts; this is the basis of the industrial spark test
Grinding wrought iron or 0.05 wt% C steel	Iron droplets with almost no dissolved carbon	Straw-yellow, ~1,800 K	Barely — long straight streaks with the occasional single fork
Magnesium or aluminium flitter	Metal vapour and oxide smoke burning around the particle	Brilliant white, ~3,000 K	No — straight, dazzling, no dissolved carbon to make CO
Titanium sponge (firework 'silver' sparks)	Titanium burning to TiO₂ with the oxide staying put	Silver-white, very bright	No — long straight needles; the branching 'titanium' sparks in fireworks are ferro-titanium, an iron alloy
Barium in a Bunsen flame test	Free Ba atoms and BaCl molecules emitting, no droplet at all	Apple-green molecular band emission at ~505–535 nm	Not applicable — there is no droplet; and BaCl needs a chlorine donor to form