Thermal Expansion Coefficient (CTE) Analysis of Cold-Sprayed Copper Components

Cold spray technology produces dense copper coatings and near-net-shape components in the solid state, making the coefficient of thermal expansion (CTE) a critical parameter for dimensional stability under thermal cycling. This article explains how the thermal expansion behavior of cold-sprayed copper parts is sampled, measured, and reported in accordance with recognized dilatometry standards such as ASTM E228, ASTM E831, and GB/T 4339. It also covers the influence of porosity, residual stress, anisotropy, and heat treatment on measured CTE values, along with typical applications in thermal management and component repair.

Technical Overview

Cold spray, also known as cold gas dynamic spraying or kinetic spraying, is a solid-state deposition process in which fine copper powder (typically 5–45 µm) is accelerated to 300–1200 m/s by a heated, high-pressure gas (nitrogen or helium) through a supersonic de Laval nozzle. Because the particles remain far below their melting point throughout the process, they bond to the substrate and to one another through severe plastic deformation and adiabatic shear instabilities rather than melting. The result is a dense, oxide-lean copper deposit that retains the chemistry of the feedstock powder while exhibiting a work-hardened, metastable microstructure with significant residual compressive stresses.

The coefficient of thermal expansion (CTE) governs how a cold-sprayed copper part grows and shrinks with temperature, and it is a decisive input for tolerance stack-ups, seal clearances, brazed and soldered joints, and thermal-fatigue life. Wrought copper expands at approximately 16.5–17.2 × 10⁻⁶/K between 20 °C and 100 °C, but in cold-sprayed deposits the effective CTE is modified by porosity (commonly 0.2–2%), residual stresses, particle-boundary bonding quality, and the layered character of the deposition process. When copper is sprayed onto lower-expansion materials such as steel (≈11–12 × 10⁻⁶/K), alumina (≈7–8 × 10⁻⁶/K), or silicon (≈2.6 × 10⁻⁶/K), even small CTE deviations translate into substantial mismatch stresses during service.

A complete thermal expansion analysis therefore combines dilatometric measurement with supporting characterization, including density and porosity, microstructure, and hardness, to deliver mean and instantaneous expansion coefficients, orientation-dependent values, cyclic stability data, and the influence of stress-relief or annealing heat treatments. Accredited third-party laboratories routinely perform this analysis to internationally recognized standards, providing data that is accepted across global supply chains.

Testing Samples

As-Sprayed Free-Standing Deposits

Free-standing coupons (for example, 60 × 25 × 10 mm plates sprayed onto sacrificial mandrels and subsequently removed) represent the intrinsic expansion behavior of the deposit without substrate constraint. Coupons are sectioned and ground into dilatometer rods of 25–50 mm length and 4–8 mm diameter or square cross-section, with end faces parallel to within 10 µm. All dimensions are measured at a reference temperature of 23 ± 2 °C, and specimens are degreased before testing to eliminate surface contamination effects.

Heat-Treated and Annealed Specimens

Companion specimens are tested after stress-relief heat treatment (typically 200–350 °C for 1–2 hours under inert atmosphere) or full annealing (450–600 °C). These conditions quantify how recovery, recrystallization, and stress relaxation alter the measured expansion response. Heat-treated data are essential when the component will serve at elevated temperature, because the as-sprayed condition rarely represents stable long-term behavior.

Orientation-Specific Anisotropy Specimens

Because cold spray builds material through overlapping passes, specimens are extracted both parallel to the deposition plane (in-plane X and Y directions) and perpendicular to it (through-thickness Z direction). Splat interfaces and layer boundaries can introduce a measurable, usually small, orientation dependence of 1–5% in the effective CTE. Confirming isotropy, or quantifying the deviation, is important for critical-dimensional applications.

Coating-on-Substrate Systems

When copper is sprayed onto aluminum, steel, titanium, or ceramic substrates, the composite system is characterized either as a whole (to obtain an effective system CTE) or through sectioned bimetallic strips tested in a thermomechanical analyzer. The evolution of substrate curvature during heating can also be used to back-calculate the mismatch strain between deposit and substrate for coating-integrity assessments.

Powder Feedstock Verification Samples

Feedstock quality directly influences deposit CTE. Representative powder samples are verified for particle size distribution by laser diffraction (ASTM B822), morphology by scanning electron microscopy, and oxygen content by inert-gas fusion analysis. Retaining feedstock records allows any anomalous dilatometric result to be traced to a powder-related cause.

Testing Items

The thermal expansion test program for cold-sprayed copper components typically includes the following measurable items:

• Mean (average) linear CTE over defined temperature intervals, for example 23–100 °C, 23–200 °C, 23–300 °C, and 23–500 °C
• Instantaneous (tangential) CTE as a continuous function of temperature
• Full thermal expansion curves of relative length change (ΔL/L₀) versus temperature
• First-cycle irreversible length change and heating–cooling hysteresis, reflecting residual stress relaxation
• Anisotropic CTE comparison between in-plane and through-thickness orientations
• Cyclic stability of the expansion response after multiple thermal cycles
• Change in CTE and dimensional stability after stress-relief or annealing heat treatments
• Supporting characterization: density and interconnected porosity by the Archimedes method (ASTM B962), microstructure per ASTM E3 and ASTM E407, and Vickers microhardness per ASTM E92 to correlate deposit condition with expansion behavior

Testing Methods

Push-Rod Dilatometry (ASTM E228)

Push-rod dilatometry is the primary and most widely accepted method for copper deposits. The specimen rod is placed in a furnace on a fused-silica or high-alumina support, and a low-force push rod transmits length change to a displacement transducer with resolution on the order of 0.05–0.1 µm. The instrument baseline is established with a blank run, and the expansion scale is verified with certified reference materials such as sapphire, borosilicate glass, or certified copper. Testing proceeds at a controlled heating rate of approximately 3 K/min under flowing argon to suppress copper oxidation, commonly from room temperature to 300 °C or 500 °C. At least two heating–cooling cycles are recorded, with the second cycle used for the reported CTE after first-cycle stress relaxation has stabilized. Repeatability of ±0.1–0.2 × 10⁻⁶/K is typically achievable.

Thermomechanical Analysis (ASTM E831)

Thermomechanical analysis (TMA) is applied when material is limited or when small coating cross-sections must be evaluated. Specimens of 2–10 mm in height are tested under a quartz probe with a small contact force, over a range extending from approximately −150 °C to 600 °C. TMA is particularly useful for through-thickness measurements of thin deposits, for screening multiple process conditions, and for sub-ambient expansion data needed in cryogenic or aerospace applications.

Absolute Interferometric Dilatometry (ASTM E289)

Laser interferometric dilatometry provides the highest accuracy and is used to resolve very small differences in expansion, to certify reference values, or to arbitrate discrepancies between laboratories. Optical fringe counting measures specimen length change without mechanical contact, with sensitivity well beyond that of push-rod systems, typically from room temperature to 500–700 °C in inert atmosphere.

Data Reduction, Quality Control, and Reporting

The mean CTE is calculated as αm = (L₂ − L₁) / [L₀ × (T₂ − T₁)], and the instantaneous CTE as α(T) = (1/L₀)(dL/dT), with the reference length L₀ defined at 20 °C or 23 °C. Reports include the full expansion curve, tabulated CTE values at regular temperature increments, the specimen orientation and heat-treatment condition, and an uncertainty budget. Procedures follow ASTM E228, ASTM E831, or ASTM E289 as applicable, with terminology per ASTM E473 and method equivalence to GB/T 4339 for metallic materials. Duplicate specimens in orthogonal orientations are recommended, and accredited third-party laboratories can issue test reports that are recognized by international customers.

Applications

Cold-sprayed copper combines very high thermal and electrical conductivity with near-net-shape additive capability and low oxide content, and reliable CTE data underpin its deployment in demanding engineering systems:

• Aerospace heat exchangers, combustor liners, and nozzle extensions subjected to aggressive thermal cycling
• Conformally cooled molds and dies for injection molding and die casting, where copper CTE must match tool-steel fixtures
• Power-electronics heat spreaders, busbars, and sputtering targets requiring predictable expansion against ceramic and silicon die
• Electromagnetic launch rails and high-current conductors with tight dimensional tolerances
• On-site repair and dimensional restoration of worn or corroded copper and copper-alloy components
• CTE-matched transitions and joints between copper and aluminum (≈23 × 10⁻⁶/K), steel (≈11–12 × 10⁻⁶/K), or ceramics, for braze design, seal-clearance definition, and thermal-fatigue prediction

FAQ

What is the typical CTE of cold-sprayed copper?

Between 20 °C and 100 °C, most dense cold-sprayed copper deposits measure approximately 16.2–17.5 × 10⁻⁶/K, which is within roughly 2–5% of wrought copper (≈16.7 × 10⁻⁶/K). The CTE rises with temperature, typically reaching 18–19 × 10⁻⁶/K near 300–400 °C.

Why does the first heating cycle differ from subsequent cycles?

As-sprayed deposits contain residual compressive stresses and a heavily work-hardened microstructure. During the first heating run, recovery and micro-yielding at particle interfaces relax these stresses, producing an irreversible length change and visible hysteresis. Standard practice is to run at least two cycles and report data from the stabilized second cycle, or to pre-condition the specimen by stress relief.

Which standards govern the measurement?

The principal methods are ASTM E228 for push-rod dilatometry, ASTM E831 for thermomechanical analysis, and ASTM E289 for interferometric dilatometry, with GB/T 4339 providing an equivalent procedure for metallic materials. Thermal-analysis terminology follows ASTM E473.

How does porosity affect the measured CTE?

Porosity slightly reduces the effective bulk expansion, roughly in proportion to its volume fraction, so 1–2% porosity typically lowers the CTE by about 1–2%. More importantly, porosity increases measurement scatter and hysteresis, which is why density per ASTM B962 is always reported alongside the CTE result.

Does heat treatment change the CTE?

Heat treatment does not change the intrinsic lattice expansion of copper, but it strongly affects the measured response. Stress relief at 200–350 °C removes first-cycle hysteresis and stabilizes dimensions, while annealing at 450–600 °C recrystallizes the deposit and improves repeatability, at the cost of reduced hardness. Heat-treated qualification data are recommended for any elevated-temperature service.

What specimen size is required for testing?

For ASTM E228 dilatometry, rods of roughly 25–50 mm length and 4–8 mm diameter or square cross-section are standard. ASTM E831 TMA accepts specimens as small as 2–10 mm. Through-thickness deposit cores of 3–6 mm thickness can be accommodated, and the testing laboratory should be consulted before specimens are cut.

Can a copper coating still attached to its substrate be tested directly?

Yes. Options include TMA of sectioned bimetallic strips with the deposit CTE derived through composite-beam analysis, or curvature-evolution measurements during heating to back-calculate the deposit–substrate mismatch strain. When the intrinsic CTE of the deposit itself is required, testing of a free-standing deposit is preferred.

To what temperature can cold-sprayed copper be tested?

Room temperature to 500 °C under flowing argon is routine. With alumina dilatometer hardware and strict inert-atmosphere control, tests can be extended to 800–1000 °C without significant copper oxidation. Sub-ambient measurement down to approximately −150 °C is possible with TMA or cryogenic dilatometry.