Measuring the Thermal Expansion Coefficient of Borosilicate

# Measuring the Thermal Expansion Coefficient of Borosilicate

Borosilicate glass has a low coefficient of thermal expansion (CTE), typically measured with a horizontal push-rod dilatometer per ISO 7991 or ASTM E228. Accurate CTE measurement governs dimensional stability, sealing compatibility and thermal-shock resistance, and serves as a core release criterion in glass production and incoming inspection. This article covers the principle, instrumentation, sample preparation, test procedure, precision control and applicable standards.

Principle & mechanism

Thermal expansion arises from the anharmonicity of interatomic vibrations. As temperature rises, the mean interatomic distance in the glass network increases, producing a measurable macroscopic length change. In borosilicate, the boron and silicon oxide network gives a characteristically low expansion. The length signal is therefore small and demands high-resolution detection. The mean coefficient of linear thermal expansion is the fractional length change per unit temperature interval over a specified range, commonly 20–300 °C. Below the strain point, expansion is nearly linear. Near and above the transformation range, the curve deviates as the glass structure relaxes. The measured curve also yields the transformation temperature from the intercept of the low- and high-temperature tangent lines. Interpreting these features requires an understanding of both the material mechanism and the measurement geometry.

Test Principle & Instrumentation

A horizontal push-rod dilatometer is the standard instrument. A cylindrical sample rests in a furnace tube. One end bears against a fixed stop while the other contacts an alumina or fused-silica push rod. The rod transmits length changes to a displacement sensor, typically a linear variable differential transformer, with resolution at the sub-micron level. A thermocouple positioned adjacent to the sample records temperature. The system applies a programmed heating rate, usually a few degrees per minute under a neutral atmosphere or flowing inert gas. The push rod and support contribute their own expansion, so an inert reference of known expansion is run under identical conditions and the sample signal is corrected accordingly. Modern instruments link displacement and temperature channels through software that computes instantaneous and mean expansion coefficients in real time and exports the full expansion curve for review.

Sample Preparation Requirements

Specimen geometry directly affects signal quality. A cylindrical or rectangular rod of 25–50 mm length and 4–10 mm cross-section is typical. Longer samples give a stronger displacement signal at the same expansion. Both end faces must be ground flat, parallel and perpendicular to the axis, since tilt or roughness introduces contact error and zero drift. Surface grinding with progressively finer abrasive, followed by cleaning with ethanol and drying, removes cutting debris and fingerprints. Annealing befOre testing relieves residual stress from machining, which otherwise distorts the early part of the curve. At least three replicate specimens from different regions of the part are recommended so that homogeneity can be judged. Samples must be free of visible bubbles, cords and striae at the measurement faces. Each specimen is measured for length at room temperature with a calibrated micrometer or caliper to 0.01 mm before loading.

Dilatometer Test Procedure

Operation begins with verification. Confirm the furnace atmosphere, purge with inert gas, and run a blank with the reference material to check baseline stability. Load the specimen with a small, constant contact force so that the rod seats firmly without stressing the glass. Set the temperature program. Hold at the initial temperature for thermal stabilization, then heat at the selected rate to the target temperature, staying below the softening point. Record displacement and temperature continuously. After the run, cool per the instrument schedule and unload the specimen. Data processing subtracts the baseline correction, computes the mean CTE over the specified interval and, where required, derives the transformation temperature from the tangent construction. Report the specimen dimensions, temperature range, heating rate, atmosphere, correction method and calculated coefficients. Any anomaly such as rod slip or curve discontinuity requires a retest with a fresh run. This procedural discipline parallels other precision dimensional methods, such as measuring hydroxyapatite coating thickness per ISO 13779-2, where technique and acceptance criteria are equally tightly controlled.

Precision, Repeatability & Calibration

Measurement uncertainty combines displacement resolution, temperature accuracy, correction fidelity and sample homogeneity. Control begins with calibration of the displacement sensor against a gauge block or micrometer-calibrated artifact, and of the thermocouple against a certified fixed-point or reference thermometer. Regular verification with a certified reference material of known expansion, such as a standard glass or sapphire, checks the complete system. Replicate runs of the same material establish within-laboratory repeatability. Practice places repeatability of mean CTE for a stable glass in the low single-digit percentage range of the value, expressed as relative scatter between repeat specimens. Sources of variance include uneven end faces, thermal gradients along the sample, heating-rate differences and incomplete baseline correction. Laboratories should maintain control charts of reference-material results, define acceptance limits for repeat testing, and re-measure when replicate specimens disagree beyond those limits.

Applicable Scenarios & Standards

Dilatometric CTE testing of borosilicate applies to incoming inspection of glass tube and rod, qualification of pharmaceutical container glass, evaluation of seals between glass and metal or between dissimilar glasses, failure analysis of thermal-shock cracking, and research into composition adjustment. It is equally relevant to component acceptance where the glass joins coatings or substrates of matched expansion. Principal reference documents include ISO 7991 for determination of the coefficient of mean linear thermal expansion of glass, ASTM E228 for push-rod dilatometry of rigid solids, and ASTM E831 for thermomechanical analysis. Product families such as borosilicate tubing are further classified by expansion requirements in their own material standards. Selecting between push-rod dilatometry and thermomechanical analysis depends on specimen size, temperature range and required precision. An accredited laboratory issues results with the temperature interval stated explicitly, since an expansion coefficient quoted without its interval is not comparable between reports.