Thermogravimetric Analysis: Watching a Sample Lose Weight

One Number, Recorded All the Way Up

A TGA run is one measurement repeated without pause: how much does this sample weigh, right now, at this temperature? A 5–20 mg specimen is spread thin in an open alumina or platinum pan so evolved gas escapes the instant it forms, on a stem reaching out of the hot zone into a sealed balance chamber near room temperature — the weighing mechanism never gets hot.

That mechanism is a null-balance electrobalance, and its defining trick is that it never lets the beam move. A vane on the beam shades an optical sensor; any deflection unbalances the photodetector pair, and a servo loop drives current through a torque coil in a permanent-magnet gap until the beam sits exactly where it started. The mass signal is that restoring current, not a displacement. Because the beam always returns to null, the stiffness and geometry of the suspension drop out of the answer, linearity holds across the full ~1 g capacity, and the instrument resolves 0.1 microgram.

Around it the furnace ramps at a programmed rate — 10 °C/min is the most common default and the rate most published curves assume, though several compositional standards specify 20 °C/min — to 1000 °C with a platinum winding, 1600 °C with silicon carbide. Two gas streams run continuously: a balance purge keeping corrosive products out of the mechanism, and a sample purge, typically ~50 mL/min of N₂ or air, sweeping products away as fast as they form.

The record is mass percent against temperature, plotted with its first derivative. That DTG curve turns each step into a peak and pulls apart overlaps a flat plot smears together. Plateaus are stable compounds; every drop is a molecule walking out.

Reading a Step as a Formula: Calcium Oxalate, Worked Through

Calcium oxalate monohydrate, CaC₂O₄·H₂O, M = 146.11 g/mol, is the teaching standard because it does three clean, well-separated things. Load 10.00 mg — 68.44 µmol of formula units — and ramp at 10 °C/min under flowing N₂.

• Near 150 °C, the water of crystallisation leaves: 68.44 µmol × 18.02 g/mol = 1.23 mg, a −12.3 % step onto a plateau at 8.77 mg. CaC₂O₄·H₂O → CaC₂O₄ + H₂O.
• Near 500 °C, the oxalate sheds carbon monoxide: 68.44 µmol × 28.01 = 1.92 mg, −19.2 %, down to 6.85 mg. CaC₂O₄ → CaCO₃ + CO.
• Near 750 °C, the carbonate calcines: 68.44 µmol × 44.01 = 3.01 mg, −30.1 %, down to 3.84 mg. CaCO₃ → CaO + CO₂.

What is left is 38.4 % of the starting mass, as CaO, and the books balance: 12.3 + 19.2 + 30.1 + 38.4 = 100.0.

Now run the logic backwards, because that is what analysis actually is. You have an unidentified white powder and the first step measures 12.3 %. Hypothesise water: 1.23 mg / 18.02 = 68.4 µmol left the pan. Divide the plateau mass by those same moles — 8.77 mg / 68.4 µmol = 128.2 g/mol — and that is CaC₂O₄ (128.10) and nothing else; divide the starting mass the same way, 10.00 / 68.4 = 146.2, and you have the monohydrate. The percentages are not a fingerprint to look up, they are stoichiometry, and for any hydrate MX·nH₂O the same step yields n = (%loss / 18.02) ÷ ((100 − %loss) / M_anhydrous).

Why a Decomposition Temperature Is Not a Constant

The third step is where most misreadings start. CaCO₃ → CaO + CO₂ is endothermic at ΔH ≈ +178 kJ/mol, with ΔS° ≈ +160.6 J/(mol·K), almost all of it the entropy of releasing a gas. Setting ΔG° = ΔH° − TΔS° = 0 on room-temperature data gives 178 300 / 160.6 ≈ 1110 K, about 840 °C; carrying the heat capacities properly moves the crossing to roughly 1170 K, so P(CO₂) reaches 1 bar at ~900 °C.

But a TGA never has 1 bar of CO₂ over the sample, because the purge removes it. Ask instead at what temperature K = P(CO₂)/P° exceeds the CO₂ pressure the sweep gas leaves behind. At 750 °C (1023 K), ΔG° = 178.3 − 1023 × 0.1606 = 14.0 kJ/mol, so K = exp(−14 000 / (8.314 × 1023)) ≈ 0.19 bar. Those room-temperature values overstate the driving force at 1023 K in the same way they underestimated the 1-bar point, so the measured decomposition pressure at 750 °C is nearer 0.1 bar; the conclusion is the same either way. Any purge holding CO₂ below roughly a tenth of a bar makes calcination spontaneous right there, and at 10⁻³ bar the threshold falls to about 820 K, near 550 °C. It runs the other way too — a deep, lidded crucible trapping its own CO₂ pushes the step back up ~100 °C.

Kinetics adds a second shift. Non-isothermal conversion follows dα/dT = (A/β)·exp(−E_a/RT)·f(α), where β = dT/dt is the heating rate. Double β and the sample spends half as long at every temperature, so the same conversion needs a hotter furnace. Differentiating the Kissinger condition sizes the shift: ΔT ≈ R T² ln2 / E_a. For a polymer step near 650 K with E_a = 200 kJ/mol that is ≈ 12 °C per doubling — the familiar ~10–20 °C rule of thumb — and because it scales as T², the same E_a at 1020 K moves a step nearly 30 °C. A decomposition temperature from a single run is therefore a procedural result, not a material constant.

Pans, Purge Gas and the Rest of the Hardware

Pan choice is chemistry, not stationery. Alumina is inert, disposable and good to ~1600 °C; platinum conducts heat better and gives the flattest baseline to about 1000 °C, but it is catalytic and forms low-melting eutectics with sulfur, phosphorus, silicon, lead and most reducing metals — one careless run turns a crucible into slag. Shape matters as much: a shallow open pan lets evolved gas leave at once, while a deep or lidded crucible builds a self-generated atmosphere that shifts every gas-releasing step upward.

Purge flow sits in a narrow window, typically 20–100 mL/min: too slow and products linger over the sample, suppressing their own reactions; too fast and you buy turbulence, baseline noise and a sample colder than the furnace reads. Switching the gas mid-run is the whole basis of compositional analysis under ASTM E1131: ramp under N₂ to separate moisture, volatiles and polymer, then switch to air at a hold so carbon black or char burns off, and weigh the incombustible ash left behind. ASTM D6370 applies that sequence to rubber, resolving oil, polymer, carbon black and ash from one 10 mg crumb; ASTM D7582 does proximate analysis of coal — moisture, volatile matter, fixed carbon, ash.

Two refinements matter. Hyphenation pipes the purge stream through a heated transfer line at 200–300 °C into an FTIR gas cell or a quadrupole mass spectrometer, so a 12.3 % step stops being an inference and becomes an identified molecule. Rate-controlled methods slow the ramp whenever |dm/dt| rises, separating steps that merge at 10 °C/min. Throughout, the thermocouple sits near the pan rather than in the sample, which is why thermal lag is always present.

Calibration, Standards and How a Result Is Specified

Mass calibration is the easy half: certified weights on the pan, per ASTM E2403, with mass-loss and residue performance verified against known decompositions under ASTM E2402 — calcium oxalate serving as the check sample precisely because its 12.3 / 19.2 / 30.1 / 38.4 ladder is pure stoichiometry.

Temperature calibration is the interesting half, because the usual trick is unavailable. You cannot drop an indium or zinc melting-point standard in the pan: melting changes no mass, so the balance sees nothing. The answer, standardised as ASTM E1582, is the Curie-point method. Put a ferromagnetic metal in the pan with a permanent magnet outside the furnace and the magnetic attraction reads as extra apparent weight; heat through the Curie temperature, the magnetism vanishes, and the balance records a sharp apparent mass loss with no chemistry whatsoever. Nickel, which loses its ferromagnetism at 354 °C, is the anchor, with alumel (~163 °C), perkalloy (~596 °C) and iron (~780 °C) bracketing the range. The size of the step is meaningless and is discarded; only its temperature is used.

Specifying a result demands a stated convention, because one curve supports several numbers: extrapolated onset (plateau crossed with the steepest tangent), T_1% and T_5%, and the DTG peak can differ by 50 °C on identical data. ISO 11358-1 governs polymers and USP General Chapter 891 covers pharmaceutical thermal analysis, and any trustworthy report states heating rate, atmosphere and flow, pan type and sample mass.

A Century of Thermobalances, and the Recipes They Overturned

Kotaro Honda, at Tohoku University, built the first true thermobalance in 1915, coupling a furnace to a chemical balance and watching manganese and calcium salts lose mass continuously rather than in the before-and-after jumps of classical gravimetry. Around 1936 Pierre Chevenard and colleagues in France built a photographically recording thermobalance, making continuous curves routine.

The consequences landed in the 1950s, when Clément Duval put roughly a thousand analytical precipitates through a thermobalance and published the curves in Inorganic Thermogravimetric Analysis (1953). The verdict was uncomfortable: a large fraction of the prescribed drying temperatures were wrong. Some precipitates had not finished losing water at the recommended temperature, others had already begun to decompose, and a few classic weighing forms had no stable plateau at all — no temperature at which their mass sat still. Gravimetric procedures were rewritten around his curves.

The modern equivalent is a reproducibility correction rather than a discovery. Published activation energies extracted by fitting a model to one heating-rate curve disagreed by hundreds of kJ/mol for the same reaction, because a single non-isothermal curve cannot separate E_a, A and f(α) — they compensate for one another almost perfectly. The ICTAC Kinetics Committee recommendations of 2011 answered by requiring isoconversional analysis across several heating rates, already codified in ASTM E1641 via the Flynn–Wall–Ozawa treatment: run four or more heating rates, fix a conversion α, and take E_a from the slope of log β against 1/T, E_a ≈ −(R/0.457)·d(log₁₀β)/d(1/T), with an iterative correction for the Doyle approximation.

How It Lies to You, and What It Is Not

Buoyancy is the classic artefact. The purge gas is a fluid and the pan displaces it. Gas density falls from ~1.2 mg/cm³ at 25 °C to ~0.3 mg/cm³ at 1000 °C, so the upthrust shrinks as the run proceeds and the sample appears to gain weight. For a pan-and-stem displacing ~0.1 cm³ that is 0.1 × 0.9 ≈ 0.09 mg — about 90 µg, nearly 1 % of a 10 mg sample and some 900 times the balance resolution. It looks like creeping oxidation; it is Archimedes. Subtract an empty blank run under identical conditions.

Sample geometry is the second trap. A large or deeply packed specimen insulates itself, lags the thermocouple and traps its own evolved gas, so steps move up and smear out; exothermic runs in air can self-heat and overshoot the programmed temperature by tens of degrees, far more for energetic samples. Static charge on the hangdown, draughts and condensables re-depositing on cool parts of the stem all make artefacts that look like chemistry — as does quoting an E_a from one heating rate.

And TGA is not DSC. Melting, glass transitions, crystallisation, curing and polymorphic transitions all move heat; none move mass, so the balance draws a flat line straight through them. The cleanest demonstration is calcium oxalate run in nitrogen and then in air: the middle step loses exactly 19.2 % in both, because CO leaves the pan either way, but the heat flow is endothermic under N₂ and strongly exothermic in air, where that CO burns as it goes. Identical TGA curve, opposite DSC curve. The converse holds too — a mass gain is real chemistry when a metal oxidises or a sorbent takes up CO₂.

Thermal-analysis techniques side by side: what each one actually records, and what it cannot possibly see

Technique	Signal recorded	Sees	Blind to
TGA (thermogravimetry)	Mass, to 0.1 microgram, versus temperature	Dehydration, decomposition, desorption, oxidative mass gain, filler and ash content, char yield	Melting, glass transition, crystallisation, polymorph changes — anything that moves heat but no mass
DSC (differential scanning calorimetry)	Heat flow to the sample minus heat flow to an inert reference	Melting, T<sub>g</sub>, crystallisation, cure, polymorphic transitions, enthalpy of reaction in J/g	Whether the sample is getting lighter at the same time
DTA (differential thermal analysis)	Temperature difference, sample minus reference	The same events as DSC, qualitatively, and usefully above 1500 °C	Quantitative enthalpy, and mass
STA (simultaneous TGA–DSC)	Mass and heat flow from one pan on one ramp	Which thermal events are mass-losing and which are not, with no run-to-run ambiguity	The identity of the molecule that left
TGA–FTIR or TGA–MS (evolved gas analysis)	Mass, plus IR spectra or mass spectra of the purge stream	Which molecule leaves at which step: water versus methanol versus CO₂	Anything that stays behind in the pan
TMA / dilatometry	Dimension change under a small applied load	Thermal expansion coefficient, softening point, T<sub>g</sub> by probe penetration	Mass and heat entirely