Determination of Thermal Conductivity of Cold-Sprayed Copper Coatings: Methods, Standards, and Appli

Thermal conductivity determination of cold-sprayed copper coatings is a key quality-control step for thermal management, electronics, and aerospace components that depend on efficient heat dissipation. This article explains the testing principles, sample preparation requirements, applicable standards such as ASTM E1461 and ISO 22007-2, measured parameters, and common questions. Understanding these procedures allows engineers to compare as-sprayed and heat-treated coatings against the reference value of bulk copper, approximately 398 W/(m·K).

Technical Overview

Cold spray, also known as cold gas dynamic spraying (CGDS), is a solid-state deposition process in which micron-sized copper powder is accelerated to supersonic velocities, typically 500 to 1100 m/s, by a compressed carrier gas such as nitrogen or helium preheated far below the melting point of copper (1083 °C). On impact, particles deform plastically and bond to the substrate without bulk melting, producing a coating with very low oxygen pickup compared with thermal spray processes that rely on melting.

Because deposition occurs in the solid state, cold-sprayed copper coatings retain a distinctive microstructure consisting of particle boundaries, a small fraction of porosity, heavily work-hardened grains with high dislocation density, and thin interfacial oxide films inherited from the powder surface. These defects scatter both electrons and phonons, so the as-sprayed thermal conductivity typically ranges from 180 to 350 W/(m·K) at room temperature, compared with about 398 W/(m·K) for annealed, fully dense oxygen-free copper. Quantifying this property is essential for design engineers who must account for the real thermal performance of the coating in service.

Thermal conductivity is rarely measured directly. Instead, it is derived from the fundamental relationship:

λ = α × ρ × cp, where λ is thermal conductivity, α is thermal diffusivity, ρ is density, and cp is specific heat capacity. Each of the three input quantities is measured independently, and the principal microstructural factors that influence the result include:

• Total porosity and pore morphology, including the ratio of open to closed porosity
• Oxide content and the continuity of oxide films at particle interfaces
• Dislocation density and residual work hardening introduced by severe plastic deformation
• Quality of particle-particle metallurgical bonding and the presence of unbonded or weakly bonded interfaces
• Post-spray heat treatment, which can restore conductivity toward bulk values through recovery and recrystallization

Testing Samples

Free-Standing Coating Specimens

The preferred configuration for accurate thermal property measurement is a free-standing coating with the substrate completely removed. A coating with a thickness of 1 to 3 mm is sprayed onto a sacrificial substrate, such as aluminum that can later be dissolved chemically, or onto a grit-blasted low-adhesion surface from which the coating can be mechanically separated. Disc specimens, commonly 10.0 mm or 12.7 mm in diameter, are then machined from the free-standing sheet. Both faces are ground flat and parallel within approximately 0.02 mm, and thickness is verified at a minimum of five locations to ensure uniformity. Specimens must be free of edge cracks and delamination, and the metallurgical condition, as-sprayed or heat-treated, must be documented because annealing significantly alters the result.

Coating-on-Substrate Specimens

When the coating is too thin to be self-supported, or when the properties of the coating in its actual deposited state on the production substrate are required, a two-layer specimen can be tested. In this approach the thermal properties of the bare substrate are measured first, and a second flash measurement is performed on the coated specimen. An inverse heat transfer analysis then extracts the coating diffusivity. This method demands excellent coating thickness uniformity, typically within ±5 percent across the measured area, and knowledge of the coating thickness by cross-sectional metallography or non-destructive means.

Sample Conditioning and Traceability

Prior to testing, specimens are degreased, dried to constant mass, and, for laser flash measurements, coated with a thin graphite film on both faces to maximize energy absorption and infrared emissivity. Sampling should be representative of the actual spray pattern, avoiding the extreme edges of the spray pass where deposition conditions differ. The test report should trace the specimen to the powder lot, carrier gas type, gas temperature and pressure, standoff distance, and any post-treatment, since all of these process variables influence thermal conductivity.

Testing Items

A complete thermal conductivity characterization of cold-sprayed copper coatings normally comprises the following measured and derived quantities:

• Thermal diffusivity α, expressed in mm²/s, measured from room temperature up to 500 °C or another specified temperature
• Specific heat capacity cp, expressed in J/(g·K), determined over the same temperature range
• Bulk density ρ in g/cm³ by the Archimedes method, together with total porosity calculated against the theoretical density of copper, 8.96 g/cm³, and the split between open and closed porosity
• Thermal conductivity λ in W/(m·K), computed at each temperature point
• Temperature-dependent conductivity curves and the conductivity recovery response after annealing at 300 to 600 °C
• Optional supporting data: electrical conductivity by eddy current per ASTM E1004 for a Wiedemann-Franz cross-check, Vickers microhardness per ASTM E384, coating adhesion per ASTM C633, coefficient of thermal expansion per ASTM E831, and metallographic image-analysis porosity per ASTM E2109

Testing Methods

Laser Flash Method

The laser flash technique is the primary method for cold-sprayed copper coatings and is performed in accordance with ASTM E1461, ISO 18755, and GB/T 22588. A short high-energy light pulse heats the front face of the disc specimen, and an infrared detector records the temperature rise on the rear face. Thermal diffusivity is calculated from the specimen thickness and the half-rise time of the rear-face temperature signal, with mathematical corrections, such as Cowan or Cape-Lehman models, applied for heat loss and finite pulse-width effects. Because copper is a very fast diffuser, a specimen thickness of 1 to 3 mm is chosen to keep the half-rise time within the measurable window. Typical measurement uncertainty is ±3 to 5 percent for diffusivity when the method is validated against certified reference materials such as isotropic graphite or high-purity copper.

Transient Plane Source Method

The transient plane source (TPS) technique, standardized in ISO 22007-2 and GB/T 32064, provides a direct measurement of thermal conductivity. A spiral sensor is clamped between two flat specimen pieces, and a controlled heating step combined with resistance monitoring yields conductivity and diffusivity simultaneously. The method is well suited to rapid quality-control screening of cold spray coupons and can be configured with one-dimensional analysis to evaluate through-thickness versus in-plane anisotropy, which arises from the layered, splat-like microstructure of cold-sprayed deposits. Specimens must be flat and large enough that the sensor is fully covered, with a combined thickness exceeding the thermal penetration depth of the test.

Specific Heat and Density Determination

Specific heat capacity is measured by differential scanning calorimetry (DSC) per ASTM E1269, ISO 11357-1, or GB/T 19466, using the comparative sapphire method over the target temperature range. Density is determined by the Archimedes immersion principle per ASTM B962, ISO 2738, or GB/T 5163, which also distinguishes open porosity through water uptake from closed porosity calculated by difference. Because density enters the conductivity calculation directly, weighing is performed on a calibrated analytical balance with oil-resistant handling for porous specimens, and measurements are repeated on multiple discs to capture spatial variability of porosity across the coating.

Data Reduction and Quality Control

Thermal conductivity at each temperature is obtained by multiplying the interpolated diffusivity, density, and specific heat values, and the combined uncertainty is propagated from all three inputs, typically yielding an overall uncertainty of ±5 to 7 percent. Accredited third-party laboratories reinforce reliability by running certified reference materials in each measurement sequence, testing duplicate specimens from different locations in the coating, and cross-checking results through the Wiedemann-Franz relation, in which thermal conductivity equals the Lorenz number (approximately 2.44 × 10⁻⁸ W·Ω·K⁻²) multiplied by electrical conductivity and absolute temperature. Significant deviation between the thermal and electrical estimates indicates interfacial thermal resistance from unbonded particle boundaries rather than simple bulk porosity effects.

Applications

Thermal conductivity data for cold-sprayed copper coatings directly support qualification and design decisions across several high-value sectors:

• Electronics thermal management, including heat spreaders, vapor chamber liners, and substrates for high-power RF and power semiconductor devices where the copper layer must conduct heat away from localized hot spots
• Aerospace propulsion hardware, such as rocket engine combustion chamber liners and nozzle extensions with integral regenerative cooling channels manufactured by cold spray on copper alloy substrates
• Electrical systems, including busbars, conductor pads, connectors, and electromagnetic interference shielding where thermal and electrical performance are coupled
• Cold spray additive manufacturing of freestanding copper parts, where measured conductivity validates the achievable property level against wrought material
• Repair and restoration of eroded or corroded copper alloy components, confirming that the repaired region restores the original heat transfer capability
• Tooling applications such as die-casting inserts and molds with conformal cooling channels, for which coating conductivity governs cycle time and thermal fatigue life

FAQ

Why is the thermal conductivity of cold-sprayed copper lower than that of bulk copper?

Porosity, oxide films at particle interfaces, unbonded particle boundaries, and a high dislocation density from severe plastic deformation all impede heat carriers. These defects interrupt the electron conduction path that dominates heat transport in copper, reducing as-sprayed conductivity to roughly 50 to 90 percent of the bulk value depending on spray conditions.

Which standards govern the measurement?

Thermal diffusivity by laser flash is covered by ASTM E1461, ISO 18755, and GB/T 22588. Transient plane source conductivity testing follows ISO 22007-2 and GB/T 32064. Specific heat is determined under ASTM E1269, ISO 11357, and GB/T 19466, while density follows ASTM B962, ISO 2738, and GB/T 5163.

What coating thickness is required for testing?

For laser flash analysis, a free-standing coating of at least 1 mm, preferably 1 to 3 mm, is recommended so that the rear-face temperature rise is measurable and correction terms remain small. For thinner coatings, a two-layer laser flash analysis on the coated substrate, or a transient plane source arrangement, is the appropriate route.

Can the coating on an actual component be tested without cutting samples?

Yes, within limits. The transient plane source method can be applied to flat, accessible coated surfaces, and two-layer flash analysis can be used on sectioned coupons. Curved surfaces, coatings under surface finish allowances, and components with complex geometry generally require witness coupons sprayed under identical parameters alongside the production part.

What measurement accuracy should be expected?

Thermal diffusivity by laser flash is typically accurate to ±3 to 5 percent, specific heat by DSC to about ±3 percent, and density by Archimedes to better than ±1 percent, giving a combined conductivity uncertainty of approximately ±5 to 7 percent when tests are performed by accredited third-party laboratories with validated reference materials.

How does post-spray heat treatment affect thermal conductivity?

Annealing between roughly 300 and 600 °C in an inert or reducing atmosphere triggers recovery and recrystallization of the work-hardened structure and improves interparticle bonding. Conductivity increases of 10 to 30 percent are commonly reported, and optimized treatments can raise cold-sprayed copper to above 95 percent of the bulk annealed value, so the heat treatment condition must always accompany the reported data.