Calculate the Parabolic Rate Constant (kp) for metal oxidation.
Parabolic Rate Constant (kp)
Understanding the Oxidation Rate of Metals
In materials science and metallurgy, the oxidation rate determines how quickly a metal or alloy reacts with oxygen to form an oxide scale. At high temperatures, this process is often diffusion-controlled, following what is known as the Parabolic Rate Law.
W² = kp · t
Where:
W is the mass gain per unit area (typically mg/cm²).
kp is the parabolic rate constant.
t is the exposure time.
Why is the Oxidation Rate Important?
Engineers use the oxidation rate to predict the service life of components in high-temperature environments, such as jet engines, power plant turbines, and industrial furnaces. A lower kp value indicates better oxidation resistance, meaning the material forms a protective scale (like Cr₂O₃ or Al₂O₃) that slows down further degradation.
Suppose a sample of Nickel-Chromium alloy is heated at 1000°C for 50 hours. After the test, the measured mass gain is 1.5 mg/cm². To find the parabolic rate constant:
Square the mass gain: 1.5² = 2.25
Divide by time: 2.25 / 50 = 0.045
The kp is 0.045 mg²·cm⁻⁴·h⁻¹
Factors Influencing Oxidation Rates
Several variables can significantly alter the oxidation kinetics of a material:
Temperature: Oxidation rates usually follow an Arrhenius relationship, increasing exponentially with temperature.
Atmosphere: The partial pressure of oxygen, humidity, and presence of contaminants like sulfur can accelerate corrosion.
Surface Finish: Rougher surfaces provide more surface area for initial reaction, though this effect often diminishes over long durations.
Alloying Elements: Adding Chromium, Aluminum, or Silicon helps form "passivating" layers that drastically reduce the oxidation rate.
function calculateOxidationRate() {
var massGain = document.getElementById('massGain').value;
var time = document.getElementById('timeElapsed').value;
var resultArea = document.getElementById('oxResultArea');
var kpDisplay = document.getElementById('kpResult');
var unitDisplay = document.getElementById('kpUnit');
if (massGain === "" || time === "") {
alert("Please enter both mass gain and time values.");
return;
}
var W = parseFloat(massGain);
var t = parseFloat(time);
if (isNaN(W) || isNaN(t)) {
alert("Please enter valid numeric values.");
return;
}
if (t kp = W^2 / t
var kp = (W * W) / t;
// Display results
resultArea.style.display = "block";
kpDisplay.innerHTML = kp.toExponential(4);
unitDisplay.innerHTML = "Units: mg² · cm⁻⁴ · h⁻¹";
// Scroll to result for better UX on mobile
resultArea.scrollIntoView({ behavior: 'smooth', block: 'nearest' });
}