X-ray thickness gauging is pivotal in online control applications, providing real-time measurements to maintain product quality and consistency. This post delves into the fundamental physics underpinning this technology, primarily the Beer-Lambert Law, which relates to the attenuation of X-rays passing through a material to its thickness. Understanding this principle is essential for effectively utilizing and optimizing X-ray thickness measurement systems in various industrial processes.

Understanding the Beer-Lambert Law

The Beer-Lambert law relates to the attenuation of photons through a material. In the case of X-ray thickness gauging, this relationship can be used to determine the thickness of a known material by shining some fixed quantity of X-ray photons through the material through a detector. Some of these X-rays will be absorbed in the material, and the rest will hit the detector. By counting these “missing” X-rays, the thickness of the material can be accurately determined.

The Beer-Lambert law is typically expressed as:

Where

Setting up the Equation: Arranging for x

Because we’re interested in the thickness of the material, we can rearrange the equation to solve for the thickness as follows:

Setting up the Equation: Defining the Constants

In the equation above, the initial intensity \(I_0\) and attenuation coefficient \(\mu\) are constants.

The initial intensity can be defined as the number of X-ray photons read by the detector with no material present. Complex variables related to the X-ray tube itself, the geometry of the measurement system, and the efficiency of the detector all contribute to the initial intensity of the measurement system. For this reason, \(I_0\) is generally measured in situ in the final machines. Also, the tube and detector efficiencies can change slightly over time, so periodic recalibration of the initial intensity is recommended.

The mass attenuation coefficient, \(\mu\), can also be thought of as a constant for a given material and measurement system. This value varies with material composition and X-ray energy, necessitating referencing databases such as the NIST X-Ray Mass Attenuation Coefficients database. For practical applications, especially with varying X-ray photon energies such as in bremsstrahlung radiation produced by an X-ray tube, integrating these tables over the energy spectrum is essential. This integration acknowledges the range of X-ray energies produced, ensuring the calculated thickness accounts for the entire X-ray spectrum. Again, because of the complexities of these calculations, in practice these numbers are often empirically defined by using coupons of the materials under test at calibrated thicknesses to calculate the mass attenuation coefficient. This can be achieved with a simple rearranging of the now-familiar formula:

By running the system with no sample, and with several samples of known thickness, we can empirically determine both the initial intensity of our measurement system, as well as the mass attenuation value for the material we’ll be measuring.

Solving for x: Calculating the Thickness

At this point in the process, we have our initial intensity, \(I_0\), and our mass attenuation, \(\mu\), defined for the material we’re testing. All that’s left now is to shine the X-rays through the sample, measure the X-rays at the detector, \(I\), plug in the variables, and solve for \(x\).

Calculating the thickness in real-time enables truly closed-loop process control in thin film production environments. The thickness can be fed back in real time to the control systems overseeing the line speed to either slow down or speed up the line to maintain the desired thickness within the required tolerance.

Why MXR’s X-Ray Tubes Excel in Thickness Measurement

MXR’s X-ray tubes stand out in thickness measurement applications due to their highly stable X-ray flux, ultra-low leakage current, and highly repeatable process. These features ensure that the initial intensity remains consistent, a crucial factor for accurate applications of the Beer-Lambert Law in real-time control systems.

Stability in X-ray flux minimizes the variability in measurements, leading to high precision, while the low leakage current reduces noise, further enhancing measurement accuracy. This combination makes MXR’s tubes exceptionally reliable for precision thickness gauging applications.

At MXR, we understand the critical importance of precise thickness measurements in maintaining product quality. Our X-ray tubes are engineered for exceptional stability and low leakage current, ensuring adherence to the Beer-Lambert Law and enabling high-precision gauging. Transform your measurement process with MXR’s reliable technology. Contact us today to find out how our X-ray solutions can refine your quality control and enhance your operational accuracy.

The post Use Case Deep Dives: X-ray Thickness Gauging appeared first on Micro X-Ray.

A Quick Refresher on EDXRF

Energy Dispersive X-Ray Fluorescence (EDXRF) is a non-destructive analytical technique used to determine the elemental composition of various materials, ranging generally from Al – U (with higher end spectrometers pushing those boundaries). A sample is excited with a primary X-ray beam, which causes a secondary beam to be emitted (or fluoresced) which is characteristic of the elements present. EDXRF collects this secondary beam, measuring the energy of each of these emitted X-rays, and collecting the X-rays into a spectrum. This spectrum is then analyzed to enable precise identification and quantification of the elements. This method stands out for its versatility, allowing analysis of solids, liquids, and powders across a wide range of concentrations, from major components to trace elements. Its key advantages include rapid analysis times, minimal sample preparation, and the ability to analyze samples in their natural state, making EDXRF a valuable tool in fields such as material science, environmental testing, quality control, and archaeological studies.

High-quality X-ray tubes, like those developed by Micro X-Ray, are crucial for achieving accurate and reliable EDXRF results. They enable more precise elemental analysis by offering optimized flux, advanced cooling methods for longer tube life, and the flexibility to adapt to various analytical needs, thereby supporting a wide array of research and industrial applications.

The Perfect Balance: 50kV/50W

Achieving the ideal balance between adequate power for a robust secondary fluorescence while avoiding detector flooding is key in EDXRF. The 50kV/50W specification serves as a sweet spot for XRF tubes, ensuring clear, distinct spectral peaks for more reliable data in around 90 seconds or less. Some applications benefit from slightly higher voltages, and some applications benefit from higher powers, but the 50kV/50W XRF tube has proven to be a standard specification in EDXRF machines for many years.

Lightbright End Window Tube: Maximizing Precision

The Lightbright end window tube, designed for precision and efficiency, features a large cone angle an ideal takeoff angle to maximize usable flux. Ultra-thin window options, as thin as 50μm, reduce low energy absorption, capturing even the subtlest spectral lines. Its end window geometry facilitates close source/sample/detector arrangements, optimizing detection efficiency. Integrated o-ring grooves support helium or vacuum purge capabilities, maintaining spectral purity and minimizing background noise.

Mini-Focus Packaged Tube: Redefining Versatility and Reliability

Our mini-focus packaged tube has been designed with an industry-standard form factor, allowing for easy drop-in replacements in both laboratory and field settings. Thanks to a proprietary oil filling technique, it can be mounted in any orientation without arcing, ensuring consistent performance. The integration of a high voltage (HV) cable reduces failure risks by removing the high voltage well connection point, enhancing device reliability and enabling quick and easy maintenance.

SeeRay: Fast Focal Spot Stabilization and Detailed Spatial Resolution

The SeeRay stands out for its rapid spot stabilization time, ideal for use with X-ray optics. Compatible with our diamond anode technology and featuring spot sizes down to 50μm and power loading up to 1.5W/μm, it enables fast, spatially resolved EDXRF measurements when combined with polycapillary optics. This capability allows for quick and detailed elemental mapping, offering a considerable advantage in both industrial and academic applications.

Extended Lifetime and Lower Total Cost of Ownership (TCO)

A pivotal factor in the selection of X-ray tubes is their operational lifetime and the subsequent total cost of ownership (TCO). Both the Lightbright and SeeRay tubes feature direct anode cooling paths, while the Mini-Focus tube utilizes an efficient oil-to-brass cooling method. These cooling approaches significantly extend the service life of our tubes beyond that of competitive offerings. A longer service life not only means lower TCO but also fewer service visits, minimizing downtime and enhancing productivity. For a deeper dive into the longevity of our X-ray tubes, please refer to our detailed blog post on how long your X-ray tube will last.

Revolutionizing EDXRF with Micro X-Ray

Micro X-Ray is dedicated to pushing the boundaries of EDXRF analysis through technological innovation and excellence. Our Lightbright end window, Seeray, and mini-focus packaged tubes are tailored to meet the varied needs of the scientific community, enhancing precision, efficiency, and innovation in analysis.

Explore the potential of our advanced tube technologies for your EDXRF applications. With Micro X-Ray, embark on a journey towards groundbreaking scientific discovery, leveraging our cutting-edge solutions to shape the future of analysis.

Thank you for considering Micro X-Ray as your partner in advancing EDXRF analysis. We are eager to support your research and development efforts with our state-of-the-art technologies.

We are here to provide the tools and insights necessary for navigating the complexities of EDXRF analysis. For further information or to discuss how our technologies can cater to your specific research needs, please don’t hesitate to reach out. Together, let’s drive innovation and achieve exceptional breakthroughs in the field of scientific analysis.

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