Femtosecond Temperature Measurements of Laser-Shocked Copper Deduced from the Intensity of the X-ray Thermal Diffuse Scattering

Metallic Materials Physics Materials Science Condensed Matter Physics
femtosecond laser copper X-ray thermal diffuse scattering temperature measurement laser shock

Academic Background

Studying the behavior of materials under extreme conditions (such as high pressure and high temperature) is an important topic in condensed matter physics and materials science. Laser shock technology can apply extremely high pressure to materials on a nanosecond timescale, while X-ray diffraction technology can capture structural changes in materials on a femtosecond timescale. However, temperature measurement in these dynamic compression experiments has always been a challenge. Traditional temperature measurement techniques (such as pyrometry) are difficult to implement on such short timescales and small-scale targets. Therefore, developing a method to accurately measure the temperature of dynamically compressed materials in a single experiment is of great significance.

The research team in this paper proposed a temperature measurement method based on the intensity of X-ray thermal diffuse scattering (TDS) using X-ray free-electron laser (XFEL) and laser shock technology. By measuring the X-ray thermal diffuse scattering intensity of copper foils under laser shock, the method deduces the material’s temperature, providing a new solution for temperature measurement in dynamic compression experiments.

Source of the Paper

This paper was co-authored by J. S. Wark and other scholars from multiple international research institutions, including the University of Oxford in the UK, Lawrence Livermore National Laboratory in the USA, and the European XFEL in Germany. The paper was published on April 21, 2025, in the Journal of Applied Physics, with the article number 137, 155904, and DOI 10.1063⁄5.0256844.

Research Process

1. Experimental Design and Objectives

The main objective of the research was to deduce the material’s temperature by measuring the X-ray thermal diffuse scattering intensity of laser-shocked copper foils. The experiment was conducted at the High Energy Density (HED) scientific instrument of the European XFEL in Schenefeld, Germany. The research team used the Dipole 100-X laser system to shock the copper foils and performed diffraction measurements on the samples using single X-ray pulses generated by the XFEL.

2. Sample Preparation and Laser Shock

The samples used in the experiment were 25-micrometer-thick copper foils, coated with a 50-micrometer layer of polyimide (Kapton) as the ablator. Laser shock was achieved using 10-nanosecond laser pulses, with energies up to 40 joules, focused on drive spots of either 500 micrometers or 250 micrometers. The laser pulse intensity was linearly modulated in the highest-pressure experiments to prevent ablation pressure decay.

3. X-ray Diffraction Measurement

During the laser shock, the research team performed diffraction measurements on the samples using 18 keV X-ray pulses generated by the XFEL. The X-ray pulses had a duration of 50 femtoseconds and an incident angle of 22.5 degrees. The diffraction signals were recorded by a pair of symmetrically placed Varex detectors, with their positions precisely calibrated using diffraction patterns from standard CeO2 powder samples.

4. Data Processing and Analysis

The diffraction data underwent a series of processing steps, including normalization to the incident X-ray flux, subtraction of the scattering signal from the ablator layer, subtraction of Compton scattering from the copper, and consideration of X-ray absorption effects in the sample. By comparing the diffraction signals before and after the shock, the research team deduced the Debye-Waller factor of the copper foils, from which the material’s temperature was calculated.

Main Results

1. Changes in Thermal Diffuse Scattering Intensity

The experimental results showed that the X-ray thermal diffuse scattering intensity of the copper foils significantly increased with increasing laser shock pressure. At a relative volume ratio (v/v0) of 0.7, the thermal diffuse scattering intensity increased by a factor of 2 to 3. This change indicates that the material’s temperature significantly rises with increasing shock pressure.

2. Derivation of the Debye-Waller Factor

By fitting the Warren model, the research team deduced the Debye-Waller factor of the copper foils under different shock pressures. This factor is closely related to the material’s temperature, and the results showed that the temperature of the copper foils exceeded 3000 K at a relative volume ratio of 0.7.

3. Comparison with Theoretical Models

The research team compared the experimental results with predictions from two thermal equations of state (EOS): SESAME 3336 and LEOS 290. The results showed that the experimental data were consistent with the theoretical predictions within the error range, validating the reliability of the method.

Conclusions and Significance

This study successfully deduced the material’s temperature by measuring the X-ray thermal diffuse scattering intensity of laser-shocked copper foils. This method provides a new solution for temperature measurement in dynamic compression experiments, with significant scientific and practical value. The experimental results demonstrate that this method can accurately measure the material’s temperature in a single experiment, offering a powerful tool for studying material behavior under extreme conditions.

Research Highlights

  1. Innovative Method: This study is the first to measure the temperature of laser-shocked copper foils in a single experiment using X-ray thermal diffuse scattering intensity, providing a new method for temperature measurement in dynamic compression experiments.
  2. High-Precision Measurement: Through precise X-ray diffraction measurements and data processing, the research team captured structural and temperature changes in materials on a femtosecond timescale.
  3. Theoretical Validation: The experimental results were consistent with predictions from two thermal equations of state, validating the reliability and accuracy of the method.

Other Valuable Information

The research team also discussed the limitations and future improvements of the method. For example, the current main source of error is the measurement accuracy of the incident X-ray flux, which could be reduced in the future by improving detector design. Additionally, this method can be applied to the study of other materials, providing more data support for research on material behavior under extreme conditions.

This study provides a new method for temperature measurement in dynamic compression experiments, with significant scientific and practical value. In the future, with technological improvements, this method is expected to be applied in more fields.