Assessing X-ray penetration is fundamental in material testing because it directly influences the ability to detect internal flaws, variations in density, and structural anomalies, all of which are critical for maintaining stringent quality standards, especially in industries like automotive and aerospace.
By calculating and knowing X-ray penetration, the process can be optimized to better visualize the internal features of tested materials and thereby enhance the overall integrity and safety of the product.
Table of Contents
Factors That Impact Penetration
There are four primary factors that influence penetration: the specifications of the X-ray tube being used, the X-ray incident angle, the density of the material being tested, and absorption in a specific combination of target and material.
Note that the X-ray voltage, current, and the working distance between the X-ray source and the material being tested have the least effect on penetration, although these factors will contribute to the intensity of the X-ray.
X-ray Tube
X-ray with higher energy penetrates deeper, and the energy is proportional to X-ray wavelength. Shorter wavelength (𝜆) X-ray has higher energy (𝛦). The unit of energy is keV, and the calculation formula is as follows.
𝛦 ≒
Incident Angle
The penetration is maximum when the X-ray is hit perpendicular to the surface, and becomes more shallow as the incident angle increases. It is important to keep in mind that when changing the incident angle during measurements, the depth of penetration will have changed.
Material Density
The atomic number and density of the material determine how much the X-rays are absorbed. Materials with higher atomic numbers, like gold and platinum, absorb more radiation, thus requiring adjustments in X-ray energy to achieve adequate penetration.
Absorption
In specific target and sample combinations, the penetration becomes more shallow by absorption due to scatter or fluorescence. One such case is that when titanium is measured with a Cu target, the penetration is almost halved compared to when a Vanadium target is used.
Assessing & Calculating X-ray Penetration
1. Select X-ray Energy Level & Analyze the Material Being Tested
These two steps are connected—you need to select the correct X-ray energy level (keV), but you must also understand the thickness of the material, the properties of the materials, and the required penetration depth to understand what energy level is suitable. As previously discussed, the material’s composition and density affect X-ray absorption, so knowing these factors helps in predicting how the material will interact with the X-rays.
Typical Penetration Combinations
Specific combinations of X-ray sources and materials are often chosen based on the energy of the X-ray and the material’s properties. Some of these standard combinations include:
Cr-Kα with Iron (αFe = 6.3 µm)
Cr-Kα has an energy level of approximately 5.41 keV. When interacting with iron, this low energy is absorbed significantly by the dense atomic structure of iron, leading to a shallow penetration depth of about 6.3 micrometers. This combination is typically used in thin-film analysis or surface analysis, where only the surface or near-surface composition is of interest.
Cr-Kα with Aluminum (Al = 15 µm)
Aluminum, being lighter and less dense than iron, allows deeper penetration of the Cr-Kα X-rays, achieving a penetration depth of about 15 micrometers. This setup is useful for analyzing slightly thicker films or layers compared to iron. It’s still primarily used for surface or near-surface analysis but allows for a deeper insight into the material compared to the penetration in iron.
Mo-Kα with Steel
Mo-Kα radiation has an energy of approximately 17.48 keV, which is higher than Cr-Kα and more ideal for internal structure analysis and phase identification in thicker metallic samples. This higher energy level allows for deeper penetration in denser materials like steel, often reaching depths of tens to a hundred microns depending on the specific alloy and its thickness.
Cu-Kα with Copper & Bronze
Cu-Kα has an energy of about 8.04 keV and is commonly used for analyzing the composition and phases within copper alloys and for corrosion studies. The exact penetration depth will vary based on the type of copper alloy used but can typically achieve depths ranging from 20 to 100 micrometers.
Ag-Kα with Ceramic or Very Dense Steel
Ag-Kα has around 22.16 keV, making it one of the best sources for applications where deeper penetration is necessary, such as when analyzing bulk ceramics or extremely thick or dense steel alloys.
2. Apply Known Mass Attenuation Coefficients
The next step in understanding and calculating X-ray penetration is to apply known mass attenuation coefficients, which represent the probability of X-ray interaction per unit mass. You can look up mass attenuation coefficients for the material’s elements from standard tables (available in resources like NIST databases). These coefficients vary with X-ray energy and material type but help determine how much X-ray beam is absorbed or scattered by the material.
3. Calculate Attenuation Coefficient
Next, multiply the mass attenuation coefficient by the density of the material to get the linear attenuation coefficient, which has units of inverse length.
4. Use the Beer-Lambert Law
Once you have the known mass attenuation and the calculated linear attenuation coefficient, you can apply the Beer-Lambert Law. This helps determine how the intensity decreases as the X-ray passes through the material.
The equation is as follows:
I= I0e- μx
In this equation, I represents the intensity of the X-ray after passing through the material thickness (x). I0 is the initial intensity, and μ is the linear attenuation coefficient.
5. Estimate Penetration Depth
Then, define a criterion for what constitutes effective penetration. Commonly used criteria include:
- Half-Value Layer (HVL): This refers to the thickness of the material at which the intensity of the X-ray beam is reduced to half of its initial value. This criterion is especially ideal when a balance between penetration and image contrast is needed.
- Tenth-Value Layer (TVL): The TVL is the material thickness at which the intensity of the X-ray beam is reduced to one-tenth of its initial value and is useful in applications requiring deep penetration, such as in thicker or denser materials.
- Limit of Penetration: The limit of penetration is the maximum thickness at which the X-rays can effectively penetrate the material and still provide usable data or images. This criterion can be particularly relevant in industrial applications where the tested materials vary significantly in thickness and density, as it helps ensure adequate penetration without overexposure.
Once you select a criterion, you can estimate penetration depth and then use it as a baseline when performing sample testing.
6. Perform Practical Testing
After calculating the estimated penetration depth, perform practical testing.
Start by choosing a sample representing the materials (and thicknesses) you intend to analyze. Ensure they’re adequately prepared by polishing, cutting, and/or removing contaminants. Then, calibrate your X-ray source so it’s emitting the correct energy and intensity, and configure focal spot size, filter settings, etc., to optimize the penetration.
Once everything is set up correctly and you’ve reviewed and understood baseline expectations, expose the sample to X-rays under controlled conditions, including setting specific exposure times based on the material and expected penetration. Use detectors or film to capture the X-rays that pass through the sample. In some setups, real-time detectors can provide immediate feedback on penetration and intensity.
Once tests are completed, analyze the captured images and data and compare the observed penetration depths and material contrasts to your theoretical predictions, making sure to identify any discrepancies and investigate potential causes, such as sample inhomogeneity, calibration errors, or miscalculations.
If the initial tests don’t match your predictions, adjust the X-ray settings, reposition the sample, or recalibrate the equipment. It may also be necessary to revise your theoretical model.
Learn More From Pulstec
Pulstec is an industry-leading manufacturer of X-ray equipment, including the μ-X360s residual stress analyzer, muraR surface hardness variation scanner, and the s-Laue and m-Laue single crystal orientation systems.
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