Slide 002: Thermal Expansion, CTE, and Annealing

Slide Visual

Slide Overview

This slide covers the coefficient of thermal expansion (CTE), glass compatibility for fusing, the three-stage annealing process, and the critical distinction between thermal stress and thermal shock. Students learn the quantitative basis for why certain glass types cannot be combined and why proper annealing prevents delayed failures.

Instruction Notes

The coefficient of thermal expansion (CTE) is the single most important number in glass working. It quantifies how much a glass expands per unit length per degree of temperature change. The formula is CTE = deltaL / (L0 x deltaT), but students need the practical implication more than the math: soda-lime glass (CTE 9 x 10^-6 /K) expands nearly three times as much as borosilicate (CTE 3.3 x 10^-6 /K) for the same temperature change. This means soda-lime glass develops much higher internal stress during cooling and is far more vulnerable to thermal shock.

CTE Compatibility in Fusing

CTE compatibility is non-negotiable in fusing work. Two pieces of glass fused together must have CTE values within approximately 5 units (on the COE scale used by art glass manufacturers) of each other. Bullseye and Uroboros are COE 90 glasses; Spectrum System 96 is COE 96. These cannot be mixed -- a difference of 6 COE units creates enough differential contraction to fracture the piece during cooling.

If a student fuses soda-lime to borosilicate, both pieces expand similarly at high temperature, but during cooling the soda-lime contracts much more. The interface between the two glasses experiences enormous shear stress -- up to 1000 psi in severe cases. The result is crazing (fine surface cracks) or catastrophic fracture -- sometimes days after the piece comes out of the kiln, making the failure seem mysterious to students who do not understand the underlying mechanism.

Compatibility testing protocol: Before committing to any project using unfamiliar glass, fuse two small test strips (1" x 3") together, anneal properly, then examine under polarized light. Stress shows as colored fringes -- no fringes means compatible; visible fringes mean reject that combination.

The Three-Stage Annealing Curve

Annealing is the controlled process of relieving internal thermal stress. The three-stage annealing curve is critical:

Stage 1 -- Heat to Annealing Point: Bring the piece uniformly to the annealing temperature. For soda-lime glass, this is approximately 960F (516C). For borosilicate, approximately 1050F (566C). The entire piece must reach this temperature uniformly -- temperature gradients at this point create new stress rather than relieving it.

Stage 2 -- Annealing Soak: Hold at the annealing point for 30-60 minutes (for standard 6mm thickness). At this temperature, the glass viscosity is approximately 10^13.4 poise -- atoms are mobile enough to rearrange and relieve stress, but the glass is rigid enough to maintain its shape. This is the "sweet spot" where stress relaxation occurs without deformation. Thicker pieces require longer soaks: 12mm needs 60 min, 25mm needs 120 min. The relationship is roughly quadratic -- doubling thickness quadruples soak time.

Stage 3 -- Controlled Cooling: Cool slowly through the strain point. For soda-lime, the strain point is approximately 900F (482C). The cooling rate between annealing point and strain point must be slow enough that temperature gradients within the glass do not regenerate stress. Standard rate: 100F/hour for 6mm thickness, 50F/hour for 12mm, 25F/hour for 25mm. Below the strain point, faster cooling is safe because the glass is rigid enough that new stress cannot form.

Annealing Schedule Reference Table

Glass Type	Annealing Point	Strain Point	Soak (6mm)	Cool Rate (6mm)	Soak (12mm)	Cool Rate (12mm)
Soda-lime	960F (516C)	900F (482C)	30 min	100F/hr	60 min	50F/hr
Borosilicate	1050F (566C)	950F (510C)	20 min	150F/hr	45 min	75F/hr
Lead crystal	860F (460C)	790F (421C)	45 min	75F/hr	90 min	35F/hr

Thermal Stress vs. Thermal Shock

The most common student mistake is cooling too fast between the annealing point and strain point. Glass that appears perfect out of the kiln may develop "delayed fracture" hours or days later when residual stress encounters a minor thermal or mechanical trigger (setting a hot cup on the piece, a draft of cold air, even a small bump).

Thermal stress is slow-acting, caused by uneven temperature distribution within the glass body during cooling. It accumulates invisibly and can persist indefinitely. Thermal shock is rapid, caused by sudden external temperature change (pulling a piece from a hot kiln into cold air). Both share the same root cause -- differential expansion within the glass body -- but thermal stress is the silent killer because there is no immediate feedback.

Key Talking Points

1. CTE is the single most important number for glass compatibility decisions
2. Soda-lime CTE (~9) is nearly 3x borosilicate CTE (~3.3) -- never mix them in fusing
3. Art glass compatibility is measured in COE units -- COE 90 and COE 96 cannot be mixed
4. CTE mismatch failures can be delayed by hours or days, making them deceptive
5. Annealing has three stages: heat to annealing point, soak, slow cool through strain point
6. The critical cooling zone is between annealing point and strain point -- this is where stress forms
7. Below the strain point, faster cooling is acceptable
8. Piece thickness determines soak time: quadratic relationship -- 2x thickness = 4x time
9. Always test unfamiliar glass combinations with small test strips under polarized light

Learning Objectives (Concept Check)

• [ ] Can the student explain what CTE measures and why it matters for glass compatibility?
• [ ] Can the student identify the three stages of annealing and their purposes?
• [ ] Can the student predict what happens when incompatible glass types are fused together?
• [ ] Can the student calculate appropriate annealing soak time for a given piece thickness?
• [ ] Can the student distinguish between thermal stress and thermal shock?

Adaptations for Different Learning Styles

Visual Learners

• Animated annealing curve: show temperature on Y-axis, time on X-axis, with colored zones for each stage (green = soak, yellow = critical cool, blue = safe cool)
• Before/after photographs of CTE mismatch failures: crazing patterns, clean fractures, delayed breaks
• Polarized light demo: show stressed glass under crossed polarizers -- stress birefringence creates vivid color patterns

Kinesthetic Learners

• Hands-on: students create their own annealing schedule for a hypothetical project using the reference table and a blank firing schedule form
• Demo: heat two mismatched glass rods, fuse them, cool quickly, and observe the break (instructor-only demo behind safety shield)
• Physical model: use two strips of different materials (metal and plastic) taped together -- bend when heated with a hair dryer to demonstrate differential expansion

Auditory Learners

• Verbal walkthrough of a complete annealing cycle: "We're at 960 degrees now. The glass is soaking. Atoms are slowly rearranging. We wait 30 minutes..."
• Discussion: "What would happen if you opened the kiln at 950F to check your piece?" (Answer: thermal shock from cold air draft)
• Story: share a real-world example of a delayed CTE failure -- a student piece that cracked three days after firing

Reading/Writing Learners

• Provide blank firing schedule worksheet: students fill in temperatures, hold times, and ramp rates for a given glass type and thickness
• Written reflection: "Describe the three stages of annealing in your own words. Why is Stage 2 called the 'sweet spot'?"
• Reference card: annealing schedules for soda-lime, borosilicate, and lead crystal at 6mm, 12mm, and 25mm thickness

Standards and References

ASTM C336 - Standard Test Method for Annealing Point and Strain Point of Glass: - Defines the precise methodology for determining annealing point (viscosity = 10^13.4 poise) and strain point (viscosity = 10^14.5 poise) - These are the reference values used in all firing schedules

ASTM C372 - Standard Test Method for Linear Thermal Expansion of Porcelain Enamel and Glaze Frits: - Applicable methodology for measuring CTE of glass and glass-based materials - Establishes the standard units and measurement conditions for CTE values

ASTM C148 - Standard Test Methods for Polariscopic Examination of Glass Containers: - Methodology for using polarized light to detect residual stress in glass - Basis for the compatibility testing protocol described in this slide

Session Details

• Time Allocation: 30 minutes (20 min presentation + 10 min annealing schedule exercise)
• Breakpoints for Discussion:
• After CTE introduction: "Which glass would survive being poured with boiling water -- soda-lime or borosilicate?" (Answer: borosilicate -- lower CTE means less expansion stress)
• After compatibility section: "A student brings you a beautiful blue glass they found at a thrift store. Can you fuse it with your Bullseye COE 90 glass?" (Answer: no -- unknown CTE, must test first)
• After annealing curve: "You're in a hurry and want to skip the soak. What's the worst that could happen?" (Answer: piece looks fine, then cracks on the way home)
• After thickness discussion: "Your project is 25mm thick. How long is the cooling phase?" (Answer: 25F/hr through 60F range = roughly 2.5 hours just for critical cool)

Discussion Prompts

1. Cost-Benefit: "Longer annealing cycles use more electricity and kiln time. How would you balance quality against cost in a production setting?"
2. Failure Analysis: "You pull a fused piece from the kiln. It looks perfect. Two days later, it cracks in half on the shelf. What happened, and what would you change?"
3. Design Constraint: "Your client wants a piece that uses both Bullseye COE 90 glass and recycled window glass (unknown COE). What do you tell them?"
4. Process Engineering: "Why do you think the annealing-to-strain-point range is only about 60F for soda-lime? What physical property of the glass determines this range?"

Instructor Notes

• The annealing curve is the single most important technical concept in this entire unit -- spend extra time here if needed
• Have a polarized light source available (two polarizing filters and a flashlight work) to demonstrate stress birefringence in real glass samples
• Common student error: confusing "annealing temperature" with "peak fusing temperature" -- emphasize that annealing happens during cooling, not during the working phase
• Keep broken/failed CTE test pieces as teaching samples -- visible failures are powerful teaching tools
• Safety: when demonstrating thermal shock (dropping hot glass into water), use a safety shield and have students stand at least 6 feet back. Flying glass fragments are a real hazard.

Common Misconceptions Corrected

• Myth: "If glass looks fine out of the kiln, the annealing worked." Reality: Residual stress is invisible to the naked eye. Only polarized light examination reveals internal stress. Pieces can look perfect and fail days later.
• Myth: "Borosilicate doesn't need annealing." Reality: Borosilicate needs less annealing time due to lower CTE, but it still requires proper annealing. Unannealed borosilicate beads commonly crack 24-48 hours after flameworking.
• Myth: "COE 90 and COE 96 are 'close enough' to fuse." Reality: A 6-unit COE difference creates significant stress. These glasses are NOT compatible. Manufacturers are very specific: use ONLY glass with matching COE ratings.

Accommodations for Neurodiversity

ADHD Support

• Provide a printed annealing schedule reference card -- students should not need to remember numbers during kiln work
• Use the polarized light demo as a visual "wow" moment to anchor the concept of invisible stress
• Firing schedule exercise provides a structured, step-by-step task with clear completion criteria

Autism Spectrum Support

• The firing schedule is inherently structured and rule-based, which many students on the spectrum find intuitive
• Provide exact numbers rather than ranges wherever possible (e.g., "100F/hour" rather than "slow cooling")
• Explain the logical chain: composition -> CTE -> annealing requirements -> schedule design

Dyslexia Support

• Use color-coded annealing curve diagram: red for heating, green for soak, blue for critical cool, gray for safe cool
• Firing schedule worksheet uses large, clear boxes for filling in values
• Avoid dense paragraphs on projected slides -- use the reference table as the primary visual

Sensory Processing Support

• Thermal shock demo (if performed) generates loud sounds -- forewarn students
• Keep kiln area well-ventilated; some students may be sensitive to the metallic smell of hot kiln elements
• Polarized light demo should use steady, non-flickering light sources

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Last Updated: 2026-03-19 Content Review: Q1 2026