The thermal expansion coefficient–temperature curve of Kovar alloy is the single most important piece of engineering data for designing reliable glass-to-metal seals in hermetic electronic packages. This article explains how the characteristic three-stage expansion curve of this iron–nickel–cobalt controlled-expansion alloy arises, how it is measured by dilatometry and thermomechanical analysis in accordance with ASTM, ISO and GB standards, and how engineers interpret the curve for seal stress evaluation and material acceptance.
Technical Overview
Kovar alloy (ASTM F15, UNS K94610, equivalent to Chinese grade 4J29) is a controlled-expansion iron–nickel–cobalt alloy containing nominally 28.5–29.5% nickel and 16.8–17.8% cobalt, with the balance being iron. The alloy was specifically developed so that its thermal expansion behavior closely matches that of borosilicate and aluminosilicate sealing glasses over the temperature range in which seal stresses are established. Because seal integrity depends on the degree of expansion matching, the coefficient of thermal expansion (CTE) as a function of temperature, typically plotted from room temperature to 600–800 °C, is the decisive quality characteristic of the material.
The CTE–temperature curve of Kovar is not linear; it displays a characteristic three-stage shape that must be understood for correct interpretation:
- Stage I (approximately 20–300 °C): The mean CTE remains low and nearly flat, typically 4.6–5.2 ×10⁻⁶/°C, because a spontaneous magnetostriction contribution partially cancels normal lattice expansion.
- Stage II (approximately 300–450 °C): As the temperature approaches the Curie point, magnetic order progressively weakens and the instantaneous CTE climbs steadily; the differential curve shows a clear inflection in this zone.
- Stage III (above approximately 450 °C): The alloy behaves as a normal paramagnetic metal and the instantaneous CTE rises sharply to roughly 10–12 ×10⁻⁶/°C, so mean CTE values computed from 20 °C increase rapidly with the upper limit of the interval.
The physical origin of the low-expansion plateau is a magnetovolume effect of the same family as the classical Invar anomaly. Below the Curie temperature (approximately 430–450 °C for Kovar), spontaneous volume magnetostriction of the ferromagnetic matrix counteracts thermal lattice expansion. Once the Curie temperature is exceeded, this compensating contribution disappears and the expansion rate increases to that of an ordinary face-centered cubic alloy. This is why specification windows for Kovar are always tied to explicitly defined temperature intervals, most commonly 20–300 °C, 20–400 °C and 20–450 °C, the latter bracketing the strain point region of the matched sealing glasses.
Typical mean linear CTE values quoted in manufacturer datasheets and material specifications are approximately:
- 20–100 °C: 5.5–5.9 ×10⁻⁶/°C
- 20–300 °C: 4.8–5.3 ×10⁻⁶/°C
- 20–400 °C: 5.1–5.5 ×10⁻⁶/°C
- 20–450 °C: 5.2–5.8 ×10⁻⁶/°C
- 20–600 °C: 7.2–7.8 ×10⁻⁶/°C
Acceptance criteria in ASTM F15 and the corresponding GB material standards for grade 4J29 restrict the mean CTE in the critical 20–450 °C window to approximately 5.0–5.6 ×10⁻⁶/°C, ensuring compatibility with common borosilicate glass families whose expansion curves run parallel to the alloy in the stress-freezing range.
Testing Samples
Rod and Bar Specimens
The reference specimen geometry for dilatometry is a machined rod of 4–6 mm diameter and 50 mm length, with the end faces ground flat, parallel to each other within 0.02 mm and perpendicular to the specimen axis. A 25 mm length may be used where instrument capacity requires it, at the cost of reduced displacement signal and slightly higher measurement uncertainty.
Strip, Sheet and Foil Specimens
Flat strip specimens are typically cut to 10–12 mm width and 50 mm length, with thickness preferably not less than 0.5 mm. Very thin foils below 0.3 mm may be tested in stacked bundles bonded at the ends, or by thermomechanical analysis, since a single layer produces a displacement signal close to the noise floor of a push-rod dilatometer.
Tubular and Wire Specimens
Tube sections and straightened wire pieces can be measured directly provided the ends are faced flat and the specimen seats squarely against the dilatometer fixture. Wire specimens should be sufficiently straightened without cold working so that elastic straightening does not contaminate the expansion signal.
Finished Components
Package headers, seal housings and other finished parts may be tested as witness specimens when the geometry allows, or the expansion behavior is verified indirectly through seal stress evaluation of representative glass-to-metal seals produced from the same lot.
All specimen categories require stress-relief annealing (typically 700–850 °C in vacuum or protective atmosphere followed by slow cooling) before measurement, because residual machining stresses relax during heating and distort the low-temperature portion of the curve. Testing is normally performed on a minimum of three specimens per lot to characterize scatter.
Testing Items
Mean Linear Thermal Expansion Coefficient
The mean CTE ᾱ between an anchor temperature (usually 20 °C or 30 °C) and a series of upper limits is the contractual acceptance parameter. Standard reporting intervals include 20–100 °C, 20–200 °C, 20–300 °C, 20–400 °C, 20–450 °C, 20–500 °C and 20–600 °C. Values are compared directly against the specification window in ASTM F15 or the GB standard for grade 4J29.
Instantaneous (Tangential) Expansion Coefficient Curve
The instantaneous CTE α(T), obtained as the derivative of the fractional length change with respect to temperature, is plotted as a continuous curve. This curve reveals the inflection near the Curie point, quantifies the slope change between stages, and allows direct graphical comparison with the expansion curve of the intended sealing glass.
Inflection Point and Curie Temperature Determination
The Curie temperature is identified from the maximum of the derivative dα/dT of the instantaneous CTE curve, or equivalently from the inflection of the ΔL/L₀ curve. A Curie temperature significantly below the normal 430–450 °C band indicates off-nominal nickel or cobalt content or excessive prior cold work.
Thermal Expansion Hysteresis
Recording both heating and cooling branches exposes hysteresis. A closed, repeatable loop after the first cycle confirms a well-annealed specimen; an open loop or a shifting baseline on the first heating indicates residual stress relaxation or oxidation and disqualifies the first run from acceptance reporting.
Curve Shape Conformity Assessment
Beyond point values, the complete curve is assessed for conformity to the characteristic Kovar shape. Abnormal features such as low-temperature steps, discontinuities, or premature steepening may reveal composition drift, martensitic transformation tendency, or a spurious oxide scale contribution.
Testing Methods
Push-Rod Dilatometry (ASTM E228)
The horizontal or vertical push-rod dilatometer is the primary method. The specimen is pressed by a low-force fused-silica or alumina rod against a fixed stop, and length change is measured by a calibrated displacement transducer. Testing is performed at a controlled heating rate of 3–5 K/min in high-purity argon or helium, or in vacuum at pressures below 10⁻² Pa for runs extending above 500 °C to suppress oxidation. Two thermal cycles are recommended, with the stabilized second heating curve used for acceptance data.
Thermomechanical Analysis (ASTM E831, ISO 11359-2)
TMA employs shorter specimens, typically 2–10 mm in length, contacted by an expansion probe under a small static load. It is well suited to thin strip and small finished parts and uses heating rates of about 5 K/min. Measurement uncertainty is somewhat higher than push-rod dilatometry because of the shorter gauge length, so TMA results are best used for comparative curve shape confirmation.
Interferometric and High-Precision Methods
Laser interferometric dilatometry (ASTM E289) measures expansion by optical fringe counting and offers the highest precision, at the level of a few times 10⁻⁹/°C in expansion coefficient resolution. It is reserved for reference-grade characterization, certification of reference materials, and research on the magnetovolume anomaly of Fe–Ni–Co systems.
Calibration, Conditioning and Data Processing
The instrument expansion baseline is verified with certified reference materials such as sapphire and platinum before each campaign. Mean CTE is computed as ᾱ = ΔL/(L₀·ΔT); the instantaneous CTE is obtained by numerical differentiation after light smoothing; the Curie point is extracted from the extremum of the derivative curve. A typical expanded measurement uncertainty for mean CTE in the 20–400 °C range is ±0.1–0.2 ×10⁻⁶/°C. Accredited third-party laboratories routinely report the full curve, tabulated mean values, test atmosphere, heating rate, specimen geometry and annealing condition together with the measurement uncertainty budget.
Applications
The expansion curve analysis of Kovar directly underwrites reliability wherever the alloy must track the expansion of a glass or ceramic across the seal-freezing temperature range. Principal application fields include:
- Hermetic glass-to-metal seal packages for transistors, hybrid microcircuits, DIP and flat-pack integrated circuit housings.
- Vacuum electron devices such as power tubes, traveling-wave tubes, klystrons and magnetrons, where pin and envelope seals must remain leak-tight through bake-out cycles.
- Reed switches and sealed relays employing matched glass envelopes around Kovar blades.
- Battery headers and glass-to-metal terminals for lithium primary cells and implantable-grade medical batteries.
- Optical and laser housings, fiber-optic feedthroughs, and pressure transducer headers requiring long-term dimensional stability.
- Ceramic-to-metal seals in which Kovar lids are joined to metallized alumina bodies, where the mean CTE up to the sealing temperature governs residual bow and solder-joint stress.
In each case, the designer overlays the measured Kovar α(T) curve on the expansion curve of the selected glass, integrates the mismatch between the seal set point and room temperature, and converts the differential strain into thermal stress using elastic constants; acceptance of the alloy lot is based on keeping that stress within a safe fraction of the glass strength.
FAQ
What is the typical mean CTE of Kovar between 20 °C and 400 °C?
A typical value is approximately 5.1–5.5 ×10⁻⁶/°C. Specification windows in ASTM F15 and the corresponding GB standard for 4J29 generally confine this interval to a band around 5 ×10⁻⁶/°C so that the alloy matches borosilicate sealing glass in the stress-freezing range.
Why does the expansion curve steepen sharply above about 430 °C?
Above the Curie temperature the ferromagnetic ordering that produces the compensating spontaneous magnetostriction disappears. The alloy then expands like an ordinary paramagnetic metal, and the instantaneous CTE roughly doubles, from about 5 ×10⁻⁶/°C to 10–12 ×10⁻⁶/°C.
Which standards govern the measurement?
Material requirements are defined by ASTM F15 and the GB standards for grade 4J29. Measurement methods are covered by ASTM E228 (push-rod dilatometry), ASTM E831 and ISO 11359-2 (thermomechanical analysis), ASTM E289 (interferometry) and GB/T 4339 for metallic materials.
Why must the first heating curve often be discarded?
Residual stresses from machining or coiling relax during the first heating, shifting the baseline and opening a hysteresis loop. A stress-relief anneal before testing plus a conditioning cycle produces a repeatable curve suitable for acceptance decisions.
How is the curve used in seal design?
The measured α(T) curve is compared with the glass expansion curve from room temperature to the glass strain point. The integrated expansion difference, multiplied by the elastic modulus and corrected for relaxation, estimates the residual seal stress; matched combinations keep this stress compressive and well below the glass fracture strength.
What specimen preparation and reporting are expected from an accredited third-party laboratory?
Laboratories should test stress-relieved specimens with flat, parallel ends, state the atmosphere, heating rate, calibration reference and uncertainty, and deliver the complete ΔL/L₀ and instantaneous CTE curves together with tabulated mean CTE values at the specified intervals, allowing direct verification against ASTM F15 or GB acceptance criteria.