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6CCVD Research

Modulation calorimetry in diamond anvil cells. II. Joule-heating design and prototypes

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2017-04-10
JournalJournal of Applied Physics
AuthorsZachary M. Geballe, Viktor V. Struzhkin, Andrew Townley, Raymond Jeanloz
InstitutionsCarnegie Institution for Science, Geophysical Laboratory
Citations2
AnalysisFull AI Review Included

6CCVD Technical Documentation & Application Brief: Diamond Anvil Cell Calorimetry

Section titled “6CCVD Technical Documentation & Application Brief: Diamond Anvil Cell Calorimetry”

Source Paper: Modulation calorimetry in diamond anvil cells II: Joule-heating design and prototypes (Geballe et al., 2017)

Executive Summary

Section titled “Executive Summary”

This research validates the use of high-frequency Joule heating modulation calorimetry within diamond anvil cells (DACs), opening new pathways for characterizing high-pressure phase transitions (e.g., melting, superconductivity). The core findings establish key material requirements critical for 6CCVD specialization:

  • High-Frequency Capability: Quantitative calorimetry requires high heating frequencies (up to 10 MHz theoretically, 300 kHz achieved experimentally with thin-films).
  • Accuracy Achieved: Absolute measurements of specific heat reached 20-30% accuracy, while thermal effusivity measurements of the surrounding glass insulation demonstrated excellent ±6% accuracy using a 50 nm Platinum thin-film heater.
  • Material Limitations: Accuracy and bandwidth are critically limited by the electrical impedance of the heater material and spurious harmonic distortion (-80 dBc) generated by measurement electronics.
  • Design Requirement: Optimal measurement accuracy is achieved using high-impedance heaters (10 Ω to 100 Ω) with precisely controlled micro-dimensions (in the 10 ”m range) to maximize the signal-to-noise ratio and bandwidth.
  • 6CCVD Value Proposition: 6CCVD’s precision MPCVD diamond fabrication, custom metalization (Pt, Ti, Au), and Boron-Doped Diamond (BDD) capabilities directly address the need for high-impedance, highly accurate integrated heaters and substrates required to replicate and extend this high-pressure thermal analysis.

Technical Specifications

Section titled “Technical Specifications”

Data extracted from numerical models and laboratory measurements.

ParameterValueUnitContext
Tested Driving Frequency Range10 Hz to 300 kHzHzLaboratory limits for high-impedance Pt thin-film
Theoretical Frequency Range100 kHz to 10 MHzHzRequired for truly adiabatic DAC calorimetry
Specific Heat Accuracy±20 to 30%Achieved for metal foils (Fe, Pt, Ni)
Thermal Effusivity Accuracy±6%Achieved for 50 nm Pt thin-film on glass
Platinum Thin-Film Thickness~50nmHeater material for high accuracy
Platinum Thin-Film Width16 ± 1”mTypical heater dimension
Iron Foil Thickness2.4 to 6”mTested foil dimensions
Spurious Harmonic Distortion-80 ± 10dBcBackground electrical noise limiting precision
Ideal Heater Impedance Range10 to 100ΩSuggested for high-accuracy semiconductor/thin-film tests
DAC Anvil Thermal Conductivity~2000W m-1 K-1Literature value for diamond (SCD)
SCD Surface Roughness RequirementRa < 1nmNeeded to minimize sample/heater contact uncertainty

Key Methodologies

Section titled “Key Methodologies”

The experimental approach utilizes high-frequency third harmonic detection (3ω) via Joule heating within DAC mock-ups to measure the thermal properties of materials.

  1. Heater Fabrication: Metal foils (Fe, Pt, Ni, 2-6 ”m thick) or thin-films (50 nm thick Pt) were prepared. Precision was achieved via techniques including razor cutting (foils) or photolithography (thin-films).
  2. Sample Assembly: The heater materials were sandwiched between layers of glass insulation (120 ”m coverslips) to create a diamond-glass-metal-glass-diamond assembly simulating the DAC high-pressure environment.
  3. Bridge Circuit Implementation: A custom electrical bridge circuit, optimized for differential measurement, was used. The circuit includes the metal sample resistor (Rsam) in one arm and a compensation resistor in the other.
  4. Joule Heating & Modulation: A sinusoidal driving voltage, Vdsin(ωt), was applied, leading to a 2ω power oscillation (Joule heating). The resulting temperature oscillation (T2ω) modulates the sample resistance.
  5. Signal Detection: The oscillating resistance generates a third harmonic voltage (V3ω) across the bridge, which is amplified and measured using a lock-in amplifier or oscilloscope.
  6. Property Inference: T2ω is inferred from V3ω, allowing calculation of total heat capacity (Ctotal) or effective thermal conductance (Kth), and consequently, specific heat (c) and thermal effusivity ($\sqrt{\rho ck}$).

6CCVD Solutions & Capabilities

Section titled “6CCVD Solutions & Capabilities”

This research highlights the absolute necessity of high-precision materials and fabrication techniques for reproducible, high-accuracy high-pressure thermal experiments. 6CCVD is uniquely positioned to address the material and dimensional challenges encountered in this work, enabling researchers to push measurement accuracy well below the current 6% limit.

Applicable Materials

Section titled “Applicable Materials”

To replicate or extend this research, 6CCVD recommends materials that support high thermal conductivity, precision heating, and optimal electrical impedance:

  • Substrate/Anvil Material: Optical Grade Single Crystal Diamond (SCD).
    • Requirement: High thermal conductivity (k ~ 2000 W m-1 K-1) is essential for defining the thermal boundary conditions (heat sink) crucial for high-frequency measurements.
    • 6CCVD Capability: We offer SCD wafers up to 500 ”m thickness, polished to achieve an atomic-scale surface finish (Ra < 1 nm), minimizing thermal contact resistance uncertainty.
  • High-Bandwidth Integrated Heaters: Boron-Doped Diamond (BDD).
    • Requirement: The paper noted that high-accuracy measurements require heater impedances between 10 Ω and 100 Ω to improve signal-to-noise ratio and bandwidth (up to 300 kHz).
    • 6CCVD Capability: We fabricate MPCVD BDD films with tunable conductivity (semiconductor to metallic), allowing researchers to design integrated heaters directly onto the SCD anvil surface that precisely meet the 10 Ω to 100 Ω requirement, circumventing the limitations of low-impedance metal foils.
  • Thin-Film Heater Components: Platinum (Pt) or Gold (Au) Metalization.
    • Requirement: Ultra-thin, precisely defined metal films (e.g., 50 nm Pt) are needed for optimal performance.
    • 6CCVD Capability: We provide custom metalization services (Au, Pt, Pd, Ti, W, Cu) allowing films to be deposited with thickness control suitable for thin-film heater applications.

Customization Potential

Section titled “Customization Potential”

The paper notes that a significant source of uncertainty (up to 10%) stems from imprecise heater sizing (±1 ”m error when cutting with razor blades or imperfect photolithography).

Research Requirement6CCVD Customization ServiceValue Proposition
Precision Geometry (Micro-dimensions, e.g., 16 ”m wide)High-resolution laser cutting and advanced photolithography services.Enables sub-micron dimensional accuracy for heater layout, drastically reducing the 10% uncertainty in volume/effusivity calculation.
Integrated Heater FabricationDirect deposition and patterning of custom metalization (Ti/Pt/Au stack) or BDD micro-structures onto polished SCD surfaces.Creates highly robust, low-contact-resistance heaters optimized for high-pressure application, minimizing electromigration risk and contact uncertainty.
Large-Scale ReplicationMPCVD PCD Wafers up to 125 mm diameter; SCD plates up to 10 mm thick.Supports scaling experiments from small DAC culets to larger volume pressure cells, as suggested in the paper for reducing heat capacity uncertainty.

Engineering Support

Section titled “Engineering Support”

6CCVD’s in-house PhD team specializes in the electrical and thermal properties of diamond materials. We can assist engineers and scientists with optimizing material selection (SCD vs. PCD vs. BDD) and heater design (impedance, metal stack, geometry) required to mitigate the -80 dBc spurious harmonic limitation and achieve the theoretical 1-10% accuracy threshold for high-pressure modulation calorimetry projects.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Part I shows that quantitative measurements of heat capacity are theoretically possible inside diamond anvil cells via high-frequency Joule heating (100 kHz-10 MHz), opening up the possibility of new methods to detect and characterize transformations at high-pressure such as the glass transitions, melting, magnetic orderings, and the onset of superconductivity. Here, we test the possibility outlined in Part I, using prototypes and detailed numerical models. First, a coupled electrical-thermal numerical model shows that specific heat of metals inside diamond cells can be measured directly using ∌1 MHz frequency, with <10% accuracy. Second, we test physical models of high-pressure experiments, i.e., diamond-cell mock-ups. Metal foils of 2-6 ÎŒm-thickness are clamped between glass insulation inside diamond anvil cells. Fitting data from 10 Hz to ∌30 kHz, we infer the specific heat capacities of Fe, Pt, and Ni with ±20%-30% accuracy. The electrical test equipment generates −80 dBc spurious harmonics, which overwhelm the thermally induced harmonics at higher frequencies, disallowing the high precision expected from numerical models. An alternative Joule-heating calorimetry experiment, on the other hand, does allow absolute measurements with <10% accuracy, despite the −80 dBc spurious harmonics: the measurement of thermal effusivity, ρck (ρ, c, and k being density, specific heat, and thermal conductivity), of the insulation surrounding a thin-film heater. Using a ∌50 nm-thick Pt heater surrounded by glass and 10 Hz-300 kHz frequency, we measure thermal effusivity with ±6% accuracy inside the sample chamber of a diamond anvil cell.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2004 - Modulation Calorimetry: Theory and Applications

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