# Modulation calorimetry in diamond anvil cells I: heat flow models

## TL;DR

This paper explores high-frequency modulation calorimetry in diamond anvil cells, demonstrating that absolute specific heat measurements are feasible at frequencies above 100 kHz, enabling detailed characterization of high-pressure phase transitions.

## Contribution

It introduces heat flow models showing that high-frequency Joule heating can provide accurate, absolute specific heat measurements in diamond anvil cells, overcoming limitations of lower-frequency and laser-heating methods.

## Key findings

- Absolute heat capacities can be measured at frequencies above 100 kHz.
- High-frequency Joule heating yields more accurate specific heat measurements.
- Laser heating introduces large temperature gradients, limiting absolute measurements.

## Abstract

Numerical simulations of heat transport in diamond anvil cells reveal a possibility for absolute measurements of specific heat via high-frequency modulation calorimetry. Such experiments could reveal and help characterize temperature-driven phase transitions at high-pressure, such as melting, the glass transition, magnetic and electric orderings, or superconducting transitions. Specifically, we show that calorimetric information of a sample cannot be directly extracted from measurements at frequencies slower than the timescale of conduction to the diamond anvils (10s to 100s of kHz) since the experiment is far from adiabatic. At higher frequencies, laser-heating experiments allow relative calorimetric measurements, where changes in specific heat of the sample are discriminated from changes in other material properties by scanning the heating frequency from $\sim 1$ MHz to 1 GHz. But laser-heating generates large temperature gradients in metal samples, preventing absolute heat capacities to be inferred. High-frequency Joule heating, on the other hand, allows accurate, absolute specific heat measurements if it can be performed at high-enough frequency: assuming a thin layer of KBr insulation, the specific heat of a 5 $\mu$m-thick metal sample heated at 100 kHz, 1 MHz, or 10 MHz frequency would be measured with 30%, 8% or 2% accuracy, respectively.