Thermal Analysis: Reading TGA, DTA and DSC Curves

Understanding Thermal Analysis in Advanced Chemistry

Thermal analysis encompasses a group of analytical techniques in which a physical or chemical property of a substance is measured as a function of temperature or time, while the sample is subjected to a controlled temperature programme in a specified atmosphere. For postgraduate and competitive examination candidates preparing for national entrance tests such as IIT-JAM, CSIR-NET, GATE Chemistry, and CUET-PG, interpreting thermal curves is an essential skill within instrumental methods of analysis.

Unlike classical benchtop gravimetry, where a precipitate is ignited to constant weight at a single static temperature, thermal methods monitor physical transformations and chemical decompositions dynamically. The three most widely used thermoanalytical techniques are Thermogravimetric Analysis (TGA), Differential Thermal Analysis (DTA), and Differential Scanning Calorimetry (DSC). To connect these dynamic techniques with classical precipitation and titrimetric principles, review our guide to the principles of gravimetric analysis.

What Each Technique Measures: TGA, DTA, and DSC

Each thermal technique isolates distinct thermodynamic and kinetic events by tracking a specific physical property of the sample against temperature (T) or time (t).

1. Thermogravimetric Analysis (TGA)

Thermogravimetric Analysis measures changes in the mass of a sample as it is heated, cooled, or held at an isothermal temperature. The sample rests inside a precision microbalance crucible positioned within an electric furnace purged with a steady stream of carrier gas (such as pure nitrogen, argon, or dry air).

• Measured Property: Sample mass (m in milligrams) or percentage remaining mass (%m).
• The TGA Thermogram: Plotted as mass (%) on the vertical y-axis versus temperature (°C or K) on the horizontal x-axis. A flat horizontal plateau indicates thermal stability across that temperature window, while a downward step indicates volatilization, desolvation, or chemical decomposition with the release of gaseous products.
• Derivative Thermogravimetry (DTG): The first mathematical derivative of the TGA curve with respect to temperature (dm/dT) or time (dm/dt). DTG curves convert gradual, sloping TGA mass-loss steps into distinct peaks. The peak maximum of a DTG curve marks the temperature at which the rate of mass loss is highest (the inflection point of the TGA step), making it straightforward to resolve overlapping decomposition reactions.

2. Differential Thermal Analysis (DTA)

Differential Thermal Analysis measures the temperature difference (ΔT = T_sample − T_reference) between the sample and a thermally inert reference material (commonly calcined alpha-alumina, α-Al₂O₃) as both are subjected to an identical heating programme.

• Measured Property: Temperature difference (ΔT in microvolts or °C).
• Thermal Mechanism: When the sample undergoes a physical phase transition (like melting) or a chemical reaction (like decomposition), it absorbs or releases enthalpy (ΔH). If the event is endothermic (ऊष्माशोषी), the sample temperature lags behind the reference (T_sample < T_reference), causing ΔT to turn negative. If the event is exothermic (ऊष्माक्षेपी), the sample releases heat (T_sample > T_reference), causing ΔT to turn positive.
• Scope: DTA is primarily qualitative or semi-quantitative because the area under a DTA peak depends strongly on instrument geometry, thermal conductivity, and packing density.

3. Differential Scanning Calorimetry (DSC)

Differential Scanning Calorimetry measures the difference in the rate of heat flow into the sample and an inert reference as a function of temperature. There are two primary DSC designs:

• Heat-Flux DSC: The sample and reference sit on a thermoelectric disk inside a single furnace. Heat flows from the furnace through the disk to both pans. The temperature difference between the two pans is monitored by thermocouples and converted mathematically into differential heat flow using the thermal resistance calibration of the disk.
• Power-Compensated DSC: The sample and reference are placed in separate, isolated micro-furnaces with independent heating elements. Whenever a thermal event occurs in the sample, the instrument adjusts the electrical power supplied to the micro-heaters to maintain both sample and reference at the exact same temperature (ΔT = 0). The difference in electrical power (ΔP = dH/dt) required to maintain isothermal conditions is measured directly.
• Quantitative Power: DSC provides direct thermodynamic values. The area under a DSC peak is directly proportional to the enthalpy change (ΔH = ∫ (dH/dt) dt), and the baseline position yields the specific heat capacity (C_p).

Interpreting DTA and DSC Curves: Peaks, Baselines, and Phase Changes

When analyzing a DTA or DSC thermogram, the first step is always to check the labeled direction of the y-axis. Different instrument manufacturers and academic literature follow different sign conventions:

• IUPAC Convention: Endothermic processes are plotted downward (negative heat flow or negative ΔT), and exothermic processes are plotted upward.
• Alternative / Legacy Convention: In some polymer characterization literature, endothermic heat flow is plotted upward (positive direction of heat absorbed into the sample). In competitive examinations, always check the directional arrow (often labeled "Exo ↑" or "Endo ↓") provided on the axis.

Endothermic versus Exothermic Transitions

Thermal transitions fall into two thermodynamic categories based on whether enthalpy is absorbed or released:

1. Endothermic Peaks (ΔH > 0):
   • Melting (Fusion): A sharp, first-order transition peak without any accompanying mass loss on the TGA curve.
   • Boiling and Sublimation: Accompanied by complete mass loss to 0% residue on the TGA curve if the sample volatilizes fully.
   • Dehydration and Desolvation: Absorption of heat to break coordination or hydrogen bonds holding solvent molecules, accompanied by stoichiometric mass loss on TGA.
   • Thermal Decomposition in an Inert Atmosphere: Non-oxidative cleavage of covalent bonds (e.g., decarbonylation or decarbonation).
2. Exothermic Peaks (ΔH < 0):
   • Crystallization: Transition from an amorphous solid or supercooled liquid melt into an ordered crystalline lattice, releasing lattice energy without any change in mass.
   • Chemisorption and Oxidation: Reaction of the sample with an active purge gas (such as air or oxygen), which may show a mass gain on TGA.
   • Combustion and Exothermic Decomposition: Rapid release of heat during oxidative degradation or decomposition of energetic compounds.

The Glass Transition (T_g): Step Shift versus Peak

A frequent point of confusion among students is distinguishing the glass transition temperature (T_g) of polymers and amorphous materials from first-order transitions like melting or crystallization.

Under the Ehrenfest thermodynamic classification, melting and crystallization are first-order phase transitions. They involve a discontinuous change in the first derivative of the Gibbs free energy (entropy and volume), resulting in latent heat (ΔH ≠ 0) that generates a distinct peak on DTA and DSC curves.

In contrast, the glass transition is an apparent second-order transition characterized by a continuous first derivative but a step-change discontinuity in the second derivative of free energy, specifically the isobaric heat capacity (C_p = ∂H/∂T). Because the heat capacity of the rubbery state above T_g is higher than that of the glassy state below T_g, the baseline of a DSC curve shifts to a new level. The glass transition appears as an endothermic baseline step (an S-shaped shift), not a sharp peak, and it occurs with zero mass loss on TGA.

Mass-Loss Steps in Hydrates: Classic Case Studies

Hydrated coordination compounds and inorganic salts exhibit structured, multi-step TGA curves that reflect the distinct chemical bonding environments of their water molecules. Water may be held as loosely bound surface moisture, lattice water trapped within interstitial voids, or coordinated water bonded directly to a central transition metal ion through coordinate covalent bonds.

1. Calcium Oxalate Monohydrate (CaC₂O₄·H₂O)

Calcium oxalate monohydrate is the universal benchmark used to calibrate thermobalances and test analytical reasoning in national examinations. When heated from ambient room temperature to 1000 °C under a controlled nitrogen atmosphere, it undergoes three cleanly separated decomposition stages:

• Stage 1 (100 °C to 230 °C): Dehydration
  CaC₂O₄·H₂O(s) → CaC₂O₄(s) + H₂O(g)
  The sample loses its single water of hydration. On the DTA/DSC trace, this corresponds to an endothermic peak.
  Theoretical Mass Loss:
  M(H₂O) / M(CaC₂O₄·H₂O) = 18.02 / 146.11 = 12.33%.
• Stage 2 (400 °C to 550 °C): Decarbonylation
  CaC₂O₄(s) → CaCO₃(s) + CO(g)
  Anhydrous calcium oxalate decomposes into calcium carbonate with the evolution of toxic carbon monoxide gas. In an inert nitrogen atmosphere, this bond cleavage appears as an endothermic DTA peak. However, if the analysis is run in air or oxygen, the evolved CO oxidizes exothermically to CO₂ (2 CO + O₂ → 2 CO₂), flipping the DTA peak from endothermic to strongly exothermic!
  Theoretical Mass Loss:
  M(CO) / M(CaC₂O₄·H₂O) = 28.01 / 146.11 = 19.17%.
• Stage 3 (650 °C to 850 °C): Decarbonation (Calcination)
  CaCO₃(s) → CaO(s) + CO₂(g)
  Calcium carbonate decomposes into solid calcium oxide (lime) and carbon dioxide. This reversible decomposition is strongly endothermic.
  Theoretical Mass Loss:
  M(CO₂) / M(CaC₂O₄·H₂O) = 44.01 / 146.11 = 30.12%.
• Final Stable Residue: The remaining white solid is pure CaO, representing 56.08 / 146.11 = 38.38% of the initial sample weight.

2. Copper(II) Sulfate Pentahydrate (CuSO₄·5H₂O)

The single-crystal X-ray structure of blue vitriol reveals that four water molecules coordinate directly to the Cu(II) ion in a square-planar geometry ([Cu(H₂O)₄]²⁺), while the fifth water molecule is uncoordinated, occupying an interstitial position held by hydrogen bonds between the sulfate oxygens and coordinated aquo ligands. This structural difference is reflected in its stepwise TGA profile:

1. The first two coordinated water molecules are eliminated between 60 °C and 110 °C to form the trihydrate: CuSO₄·3H₂O.
2. The next two coordinated water molecules are eliminated between 110 °C and 150 °C to yield the monohydrate: CuSO₄·H₂O.
3. The fifth, strongly hydrogen-bonded lattice water molecule requires higher thermal energy, desorbing between 200 °C and 250 °C to leave anhydrous white CuSO₄.
4. Above 700 °C, anhydrous CuSO₄ undergoes chemical decomposition into black copper(II) oxide (CuO) with the evolution of sulfur trioxide and sulfur dioxide gases (SO₃ and SO₂).

Stoichiometric Calculations from TGA Curves

Quantitative analysis of TGA curves relies on conservation of mass. By measuring the percentage mass loss (Δm%) across a defined temperature plateau, one can calculate molecular weights, numbers of coordinated solvent molecules, or the percentage purity of a sample. When reporting experimental mass measurements, always adhere to strict rules of measurement uncertainty as detailed in our guide to error analysis and significant figures.

The Governing Formula

For a decomposition reaction where an initial solid reactant A releases a volatile gaseous component B leaving a solid residue C:

A(s) → C(s) + n B(g)

The observed percentage mass loss (Δm%) is related to the molar masses by:

Δm% = (Δm / m_initial) × 100 = (n × M_B / M_A) × 100

Where:

• Δm = absolute mass lost during the step (mg)
• m_initial = starting mass of the sample before the step (mg)
• M_B = molar mass of the evolved volatile fragment (g/mol)
• M_A = molar mass of the starting compound (g/mol)
• n = stoichiometric coefficient (number of moles of volatile fragment per mole of starting compound)

Worked Example 1: Calculating the Hydration Number (x)

Problem: A 28.50 mg sample of hydrated nickel(II) chloride, NiCl₂·xH₂O, is heated in a platinum crucible under dry nitrogen. A single continuous dehydration step is observed between 80 °C and 210 °C. The mass stabilizes at a horizontal plateau of 15.53 mg. Above 600 °C, no further mass loss occurs. Determine the value of x. (Atomic weights: Ni = 58.69, Cl = 35.45, H = 1.008, O = 16.00 g/mol).

Step-by-Step Solution:

1. Calculate the mass of water lost:
   Mass of water lost (Δm) = m_initial − m_anhydrous = 28.50 mg − 15.53 mg = 12.97 mg.
2. Calculate the molar masses:
   M(NiCl₂) = 58.69 + (2 × 35.45) = 129.59 g/mol.
   M(H₂O) = (2 × 1.008) + 16.00 = 18.016 g/mol.
3. Find the moles of anhydrous NiCl₂ residue:
   Moles of NiCl₂ = 15.53 mg / 129.59 mg/mmol = 0.11984 mmol.
4. Find the moles of evolved H₂O:
   Moles of H₂O = 12.97 mg / 18.016 mg/mmol = 0.71992 mmol.
5. Determine the stoichiometric ratio x:
   x = moles of H₂O / moles of NiCl₂ = 0.71992 / 0.11984 = 6.007 ≈ 6.
   The molecular formula of the hydrated salt is NiCl₂·6H₂O.

Worked Example 2: Determining Purity in a Binary Mixture

Problem: A 40.00 mg sample consisting of calcium oxalate monohydrate (CaC₂O₄·H₂O, M = 146.11 g/mol) mixed with an inert, thermally stable silica (SiO₂) filler is analyzed by TGA. The mass-loss step between 100 °C and 220 °C corresponding to complete dehydration measures 3.95 mg. Calculate the mass percentage of CaC₂O₄·H₂O in the original mixture.

Step-by-Step Solution:

1. Determine the moles of water evolved:
   Moles of H₂O = 3.95 mg / 18.016 mg/mmol = 0.21925 mmol.
2. Relate water loss to calcium oxalate monohydrate:
   Each mole of CaC₂O₄·H₂O releases exactly 1 mole of H₂O during this stage.
   Moles of CaC₂O₄·H₂O = 0.21925 mmol.
3. Calculate the mass of CaC₂O₄·H₂O in the initial mixture:
   Mass = 0.21925 mmol × 146.11 mg/mmol = 32.035 mg.
4. Calculate the percentage purity:
   Percentage = (32.035 mg / 40.00 mg) × 100 = 80.09%.

Experimental Factors That Alter Thermal Curves

Thermal curves are not absolute physical constants; they depend on both operational parameters and sample characteristics. Understanding these variables prevents misinterpreting artifacts during exam problems and laboratory research:

• Heating Rate (β = dT/dt): Faster heating rates (e.g., 20 °C/min vs. 2 °C/min) cause thermal lag across the sample bed. Decomposition onsets and peak temperatures shift toward higher values, and closely spaced consecutive transitions can merge into a single broad peak. Slower heating rates optimize peak resolution.
• Atmosphere Composition: Purging with an inert gas (N₂, Ar) prevents oxidation and allows purely pyrolytic decomposition. An oxidizing atmosphere (air, O₂) shifts decomposition temperatures downward and converts endothermic pyrolysis reactions into vigorous exothermic combustion peaks. Furthermore, purging with a decomposition product gas (e.g., running CaCO₃ calcination under a pure CO₂ atmosphere) suppresses decomposition until significantly higher temperatures according to Le Chatelier's principle.
• Sample Mass and Particle Size: Large sample masses create thermal gradients between the outer surface and the crucible core. Coarsely ground crystals impede the diffusion of evolved gases out of the particle interior, shifting the apparent decomposition onset upward. Uniformly powdered samples packed thinly ensure reproducible heat and mass transfer.
• Crucible Geometry and Material: Open pans allow rapid gas escape, while crimped pans with laser-drilled pinholes maintain self-generated partial pressures of volatile components. Reactive crucibles (such as aluminum pans used above 550 °C or platinum pans used with phosphorus-containing compounds) can catalyze reactions or alloy with the sample.

Syllabus-Based Examination Strategy for Chemistry Aspirants

Thermal analysis is regularly examined across national chemistry tests in India, including IIT-JAM, CSIR-NET (Chemical Sciences), GATE Chemistry (CY), and CUET-PG. Because the weightage, section distributions, and question formats vary across testing cycles, aspirants should avoid relying on fixed frequency claims. Instead, treat thermal methods as a core analytical topic in your preparation plan.

When solving thermal analysis problems in competitive examinations:

1. Inspect axes immediately: Confirm whether mass or derivative mass is plotted on TGA, and identify whether exothermic heat flow is plotted upward or downward on DTA/DSC.
2. Correlate techniques: If a DTA peak appears without a corresponding TGA mass-loss step, identify it as a physical transition (melting, crystallization, or solid-state phase change). If a mass-loss step aligns with an endothermic DTA peak, identify it as desolvation, volatilization, or thermal cleavage.
3. Calculate mass losses systematically: Always write down the balanced chemical equation, determine the molar mass of the expelled gaseous fragment, and compute theoretical percentage drops before matching with experimental TGA curves.
4. Confirm exam details from official sources: Always download the latest official brochures and syllabus notifications for your target examination. Build your own tally of recurring concept areas by working directly through official previous year question papers.

For rigorous classroom-centre instruction or interactive ONLINE classes covering physical, inorganic, and analytical chemistry for IIT-JAM, CSIR-NET, and GATE, explore our structured analytical chemistry study material or speak with Mr. Aniket Bhardwaj (founder, 20+ years teaching chemistry) at 9212142427.

Frequently Asked Questions

What is the primary operational difference between DTA and DSC?

Differential Thermal Analysis (DTA) measures the temperature difference (ΔT) between the sample and an inert reference under identical heating conditions, making it primarily qualitative or semi-quantitative. Differential Scanning Calorimetry (DSC) measures the differential heat flow rate (dH/dt) required to maintain both sample and reference at the same temperature or monitors heat flux across a calibrated thermal resistor. DSC yields direct, highly accurate quantitative thermodynamic data, including enthalpy changes (ΔH) and heat capacity (C_p).

Why does the glass transition appear as a baseline step rather than a peak on DSC?

The glass transition (T_g) is an apparent second-order thermodynamic phase transition that does not involve latent heat (ΔH = 0). As an amorphous material transitions from a rigid, glassy state to a flexible, rubbery state, its heat capacity (C_p) increases abruptly. Because heat flow in DSC is directly proportional to heat capacity, this sudden increase in C_p shifts the recorded baseline upward or downward (depending on axis convention) into an S-shaped step, rather than forming an endothermic or exothermic peak.

How does changing the purge gas from nitrogen to air alter calcium oxalate decomposition?

In an inert nitrogen atmosphere, the second decomposition stage (loss of carbon monoxide: CaC₂O₄ → CaCO₃ + CO) is endothermic because thermal energy is consumed to cleave the carbon-carbon and carbon-metal bonds. When the analysis is performed in air or oxygen, the evolved carbon monoxide gas undergoes immediate catalytic oxidation to carbon dioxide (2 CO + O₂ → 2 CO₂). This highly exothermic gas-phase reaction overwhelms the endothermic bond cleavage, flipping the second DTA/DSC peak from endothermic to strongly exothermic.

Why do higher heating rates shift decomposition temperatures to higher values?

Higher heating rates (e.g., 20 °C/min compared to 2 °C/min) introduce thermal lag, where the internal temperature of the sample lags behind the furnace thermocouple temperature due to finite thermal conductivity. Furthermore, chemical decomposition kinetics require a finite time for nucleation, bond cleavage, and gas diffusion out of the sample bed. When the furnace heats rapidly, the sample reaches higher nominal furnace temperatures before the reaction completes, shifting the observed onset and peak maximum upward.

Can TGA detect melting points or glass transitions?

No. TGA only detects events that involve a change in sample mass, such as desolvation, volatilization, sublimation, thermal degradation, or gas-solid chemisorption. Pure physical phase transitions such as melting, crystallization, and glass transitions occur at constant mass (Δm = 0) and do not produce steps on a TGA thermogram. These non-mass-loss transitions must be detected using DTA or DSC.

What is Derivative Thermogravimetry (DTG) and why is it used?

Derivative Thermogravimetry (DTG) plots the first mathematical derivative of mass change with respect to temperature or time (dm/dT or dm/dt). While standard TGA curves show gradual, sloping weight-loss steps that can overlap when consecutive reactions occur close together, the DTG curve converts each step into a sharp peak. The peak maximum identifies the exact temperature of maximum decomposition rate (inflection point), allowing chemists to resolve overlapping thermal degradation events and determine onset and completion boundaries accurately.