Lead-free multilayer capacitors reached an energy density of 3.7 ± 0.2 J cm⁻³ across a 170 K temperature span, from −60 °C to 110 °C, at an electric field of 306 kV cm⁻¹. That figure describes how much energy can be harvested for each cubic centimetre of device material. Direct and indirect measurements gave consistent results in tests of barium strontium titanate, or BST, devices designed for heat-to-electricity conversion through Olsen cycles.
A direct test matched the estimate
Researchers checked the indirect calculation with an 80 K direct Olsen cycle, recording voltage and current over time while the device was charged and discharged. The cycle produced 30 mJ net, equal to 1.9 J cm⁻³. Under the same conditions, the indirect cycle yielded 2.0 J cm⁻³. In that indirect approach, energy density is calculated from the area between two isothermal D–E loops measured at different temperatures.
Most of the gain came in a narrow band
The broad 170 K result hides a sharper operating window. When the range was divided into 10 K steps, the largest increase in energy density was 0.23 ± 0.02 J cm⁻³ between 40 °C and 50 °C. By contrast, the increase between 100 °C and 110 °C was only 0.001 J cm⁻³. The device therefore had a wide overall range, but its incremental output varied sharply with temperature.
The researchers linked the peak to BST’s electrical phase behavior. In zero electric field, the material showed a diffuse second-order ferroelectric-to-paraelectric transition, with a Curie temperature of 18 °C. The authors interpreted the higher energy peak at 40 °C to 50 °C as a field-induced upward shift of that transition.
Efficiency remained modest in the full cycle
Energy density is not the same as efficiency. For a cycle from −10 °C to 90 °C, the net output efficiency reached 0.98%. When the result was scaled against the Carnot efficiency, an idealized heat-engine benchmark, it was 6.7% for the same cycle. The scaled figure rose to 24.3% for the narrower 40 °C to 50 °C interval.
Performance depended on the comparison conditions
BST was not consistently ahead of the PST benchmark. Over 175 K at 195 kV cm⁻¹, BST reached 2.9 J cm⁻³, compared with 4.4 J cm⁻³ reported for PST. In another comparison covering 155 K, the two materials both reached 3.6 J cm⁻³, but the BST device was tested at 306 kV cm⁻¹ and the PST device at 145 kV cm⁻¹. The figures do not establish a blanket advantage for BST across operating conditions.
A layered ceramic device
The capacitors were built as multilayer ceramic devices with 11 BST ceramic layers and 10 platinum electrode layers, plus two inactive protective BST layers. The active portion accounted for 50% of the total volume. Average thicknesses were 36 µm for a BST layer and 1.6 µm for an electrode.
Fabrication used solid-state reaction and tape casting, followed by binder burnout at 500 °C for 24 hours and sintering at 1350 °C for four hours in air.
High-temperature durability remains the harder test
At 306 kV cm⁻¹, leakage current was as low as 0.05 µA below 100 °C, and all 10 tested capacitors withstood at least 300 kV cm⁻¹ without electrical breakdown. The reported stability analysis, however, set a 60 °C temperature limit for its long-cycle protocol. Cycling from −60 °C to 60 °C at 140 kV cm⁻¹ produced approximately 1.5 J cm⁻³. That stability result stops below the 110 °C used for the maximum energy-density measurement.
The project received funding from the European Research Council under the European Union’s Horizon Europe programme through grant agreement No. 101141445 ELEC_FROM_HEAT. The authors declared no conflicts of interest.
Paper data and sources
Original title: Heat-to-Electricity Conversion Using Barium Strontium Titanate Multilayer Capacitors.
Authors: Fan Ni, Junning Li, Uros Prah et al.
Journal/Repository: Advanced science (Weinheim, Baden-Wurttemberg, Germany)
Status: Peer-reviewed
First online: 2026-08-21
DOI: 10.1002/advs.77106
Original paper