Machine Learning Reveals Links Between Surface Texture and Liquid Behaviour on Metal Alloys

Researchers are increasingly investigating copper-silver (CuAg) alloys for advanced electrical and electronic applications due to their favourable conductivity and strength properties. Krzysztof Wieczerzak and Grzegorz Cios, both from the Department of Materials Science, Faculty of Mechanical Engineering and Aeronautics at Rzeszow University of Technology, led a collaborative study with Piotr Bała of the Faculty of Metals Engineering and Industrial Computer Science, AGH University of Krakow, Johann Michler working with colleagues at the Academic Centre for Materials and Nanotechnology, AGH University of Krakow, and Benedykt R. Jany from the Marian Smoluchowski Institute of Physics, Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University. This interdisciplinary team explored the relationship between surface texture, composition, wetting behaviour, and optical characteristics of Cu, Ag, and CuAg thin films deposited on silicon substrates. By employing data mining and machine learning, the study reveals robust links between surface morphology and wetting properties, offering a pathway to engineer tailored material performance through precise control of texture morphology.

CuAg alloys are particularly noted for their superior electrical conductivity, a key requirement in applications such as electrical connectors and components operating in high-conductivity environments.

Furthermore, CuAg alloys exhibit good thermal conductivity, facilitating effective heat dissipation in electronic devices. Although not among the strongest metallic materials overall, CuAg alloys offer a favourable trade-off between electrical conductivity and mechanical strength. Their hardness and tensile strength can be substantially increased relative to pure copper or silver, depending on the chemical composition, phase structure, and thermo-mechanical treatment.

Cold deformation and directional solidification techniques can further improve their mechanical performance. Notably, the addition of silver results in the formation of nano-sized Ag precipitates, contributing to strengthening through solid-solution and precipitation hardening mechanisms. Incorporating zirconium (Zr) into CuAg alloys produces multicomponent materials, including CuAgZr metallic glasses (MGs).

The amorphous structure of these MGs results in distinct combinations of strength, ductility, and viscoelasticity, characteristics absent in conventional crystalline alloys. Examining the relationship between surface texture morphology, like roughness and contact angle, a measure of wettability, is essential. Different textures (square, circular, hemispheric, and triangle) processed on metal alloy surfaces exhibit varying structural accuracy and surface morphology.

Square textures demonstrate the highest accuracy and contact angle, while triangle textures display the worst formation quality due to the stepping effect mechanism. The surface texture morphology also influences the optical properties of metal alloys, affecting characteristics including roughness, glossiness, colour, and reflectivity. Utilising data mining and machine learning techniques, they identified robust correlations between contact angle and surface fractal dimension across all layer types, promoting Cassie-Baxter surface state formation.

Analysis revealed a significant connection between layer thickness and surface topography entropy deficit, suggesting a dynamic evolution of surface order/disorder during metal film growth. Furthermore, contact angle sensitivity to layer thickness implied a correlation with microstructure evolution. Through K-Means clustering, the formed surface textures morphology was successfully categorized.

A Random Forest regression model was developed to accurately predict water contact angles (Mean Absolute Error around 5 deg) using only texture and optical parameters. The model, along with accompanying Python code, is publicly available. The copper concentration, also determined by XRF, spanned from 10 to 90 at.% within the CuAg alloy layers, demonstrating a comprehensive compositional range. Analysis of X-ray diffraction (XRD) patterns showed a clear structural transition from pure silver to pure copper as copper content increased.

Specifically, the silver diffraction peak at approximately 38.15° broadened and shifted to higher 2θ angles with increasing copper, indicative of solid solution formation and reduced crystallite size. This peak diminished around 60 at.% copper, coinciding with the emergence of a copper reflection at 43.35°, aligning with the established Cu-Ag binary phase diagram.

Subsequent scanning electron microscopy transmission Kikuchi diffraction (TKD) analysis provided detailed crystallographic grain properties. Inverse pole figures for CuAg-1 and CuAg-9 samples confirmed grain size variations, with measurements establishing a decreasing trend in grain size as copper concentration increased. Quantitative analysis showed that the average grain size diminished with higher copper content, while conversely, grain size increased proportionally with increasing layer thickness.

These TKD measurements, calculating grain size as the equivalent circle diameter and using area-weighted means, revealed a clear correlation between layer thickness and crystallographic grain dimensions. A DC magnetron sputtering system served as the core of the film deposition process, fabricating copper, silver, and copper-silver alloy thin films on textured silicon substrates.

High-purity copper (99.99% purity, HMW Hauner GmbH) and silver targets were employed in a co-sputtering configuration within a vacuum chamber (Korvus Technology, United Kingdom), allowing for precise control over alloy composition. Maintaining a base pressure of approximately 1 × 10-6 mbar, the chamber utilised argon gas (99.9999% purity) at a working pressure of 1 × 10-2 mbar, ensuring high-quality film growth.

Samples were patterned into nine discrete 5mm diameter circular slices using a stainless steel mask, facilitating localized analysis across a thickness gradient. The substrate-target distance was carefully regulated to establish a pronounced thickness gradient for both copper and silver films, and a compositional gradient within the copper-silver library.

Deposition powers of 82W and 57W were applied to the copper and silver targets respectively, with each deposition process lasting one hour and repeated three times on identical silicon wafers to ensure reproducibility. Following deposition, material composition and film thickness were quantified using X-ray fluorescence (XRF) spectrometry (Fischerscope X-Ray XDV-SDD, Fischer, Sindelfingen, Germany), employing a 50kV beam energy and a 0.33mm spot size for accurate measurements.

Structural characterisation, including phase identification, was then performed via X-ray diffraction (XRD) using a D8 Discover diffractometer (Bruker, Billerica, USA) with both CuKα1 (λ = 1.5406 Å) and CuKα2 (λ = 1.54439 Å) radiation, providing comprehensive crystallographic information. Scientists have long sought to engineer surfaces with precisely controlled wetting properties, crucial for applications ranging from self-cleaning materials to microfluidic devices.

This work represents a significant step forward, not simply because it demonstrates a predictive link between surface texture and water behaviour, but because it establishes a robust methodology for achieving that control. For years, the challenge has been disentangling the complex interplay of factors, composition, morphology, and deposition conditions, that govern how liquids interact with solid surfaces.

Simply creating a rough surface isn’t enough; the type of roughness matters immensely. The power of this research lies in its integration of materials science with data science. By employing machine learning algorithms, the researchers moved beyond empirical observation to identify quantifiable correlations between measurable parameters like fractal dimension and contact angle.

This predictive capability is particularly valuable, offering a pathway to ‘design’ surfaces with specific wettability characteristics without relying on laborious trial-and-error experimentation. The publicly available Python code further accelerates this process, democratising access to advanced surface engineering techniques. However, the study focuses on relatively simple metal films deposited on silicon. The copper concentration, also determined by XRF, spanned from 10 to 90 at.% within the CuAg alloy layers, demonstrating a comprehensive compositional range. Analysis of X-ray diffraction (XRD) patterns showed a clear structural transition from pure silver to pure copper as copper content increased.

Specifically, the silver diffraction peak at approximately 38.15° broadened and shifted to higher 2θ angles with increasing copper, indicative of solid solution formation and reduced crystallite size. This peak diminished around 60 at.% copper, coinciding with the emergence of a copper reflection at 43.35°, aligning with the established Cu-Ag binary phase diagram.

Subsequent scanning electron microscopy transmission Kikuchi diffraction (TKD) analysis provided detailed crystallographic grain properties. Inverse pole figures for CuAg-1 and CuAg-9 samples confirmed grain size variations, with measurements establishing a decreasing trend in grain size as copper concentration increased. Quantitative analysis showed that the average grain size diminished with higher copper content, while conversely, grain size increased proportionally with increasing layer thickness.

These TKD measurements, calculating grain size as the equivalent circle diameter and using area-weighted means, revealed a clear correlation between layer thickness and crystallographic grain dimensions. The observed increase in grain size with layer thickness is consistent with typical behaviour in sputter-deposited thin films. These findings establish a fundamental link between alloy composition, layer thickness, and resulting microstructural characteristics.