In the field of materials science and engineering, accurate measurement of coating thickness is crucial for evaluating product performance, controlling process quality, and ensuring coating functionality. This measurement task becomes particularly complex when the surface of the substrate has significant roughness. The inherent peak-valley structure of rough surfaces obscures the physical interface between the coating and the substrate, and measurement methods that traditionally rely on clear interface localization face the fundamental problem of datum determination in such scenarios. Misjudgment of the datum will directly lead to systematic deviations in thickness measurements, which in turn will affect the reliable evaluation of key attributes such as wear resistance, corrosion resistance, and bond strength of the coating.
Definition of datum
To address these challenges, it is first necessary to clearly define the coating thickness datum for rough substrates. Often, the datum is not a real physical interface, but rather a reference plane for calculations. At present, there are two main theoretical models:
Contour midline datum model: The model defines the arithmetic mean midline of the original rough contour of the matrix as the datum. Coating thickness is defined as the average vertical distance from the surface of the overlay to the midline. Suppose that the original matrix contour function is z_b(x) and its arithmetic mean midline is m(x), satisfying ∫ [z_b(x) - m(x)]dx = 0 (within the evaluation length). The average thickness of the coating can be expressed as t_c:
t_c = (1/L) ∫ [z_c(x) - m(x)] dx
where z_c(x) is the surface profile function after coating, and L is the evaluation length.
Envelope Reference Model: The model uses the peak envelope of the substrate profile as the datum. This model focuses more on evaluating the coating's coverage of the matrix peaks, and is suitable for scenarios where the thinnest coating point or coating continuity is concerned. Thickness is defined as the distance from the coating surface to this envelope.
The choice of model depends on the purpose of the measurement, the coating process (e.g., whether the valley is completely filled), and the subsequent performance analysis needs.
Measurement method
Different physical measurement methods have different ways of determining the datum. The following are common techniques for rough matrices and their datum treatment strategies.
Microscopy
The specimen section is prepared by cutting, mosaic, and polishing, and is observed under an optical microscope or scanning electron microscope. Determination of datum is a critical step:
Image preprocessing: The digital image of the acquired section is filtered to reduce noise interference such as scratches introduced by sample preparation.
Interface recognition: Based on the grayscale gradient or edge detection algorithm, the transition area between the coating and the substrate is preliminarily identified.
Baseline fitting: In the substrate area (usually the undisturbed part of the substrate below the coating), a straight line or curve is fitted as a reference line in the direction parallel to the coating surface. For rough substrates, the trend line of the matrix contour is usually fitted by the least squares method as the projection of the datum on the cross-section.
Thickness Calculation: The average of these vertical distances is calculated from the vertical leads to the baseline at each point on the outer surface of the coating as the thickness.
stylus contour method
The probe is passed through the coating surface to record the profile curve. Measuring coating thickness on a rough substrate typically requires two scans:
Scan the uncoated surface of the original substrate to obtain a contour curve R_b (x).
Scan the coated surface to obtain the contour curve R_c (x).
Benchmarks align: Utilize the same unpainted datum area in both scans or contour alignment via software algorithms to ensure consistent horizontal coordinates.
Thickness Calculation: At the same horizontal coordinate x, the local thickness of the coating d(x) = R_c(x) - R_b(x). However, this difference includes matrix roughness. Therefore, the statistical mean of d(x) within the evaluation length is usually calculated, or the midline of R_b(x) is used as the datum to eliminate the influence of roughness fluctuations.
Eddy current method and ultrasonic method
These non-destructive methods are based on electromagnetic or acoustic principles. For rough substrates, their datum is indirectly determined by a calibration procedure:
The instrument is calibrated using a series of standards of known thickness (placed on a substrate of similar roughness to the DUT) to establish a curve between the signal response (e.g., voltage, phase) and thickness.
The calibration process essentially builds the average effect of a specific roughness matrix (i.e., the equivalent datum) into the calibration curve.
When measuring, the signal value read by the instrument is derived from the thickness value through the calibration curve, which corresponds to the thickness based on the statistical average surface of the rough matrix.
Influencing factors
When determining a datum, the following factors must be considered and corrected or explained accordingly:
| Matrix roughness parameters | Ra, Rz and other values directly affect the datum position. The thickness should also indicate the roughness of the matrix. |
| Coating penetration and filling | The coating material may penetrate into the matrix pores or depressions, causing the physical interface to be lower than the original matrix peak top line. |
| Measurement location and statistics | The measurement results at different locations on rough surfaces have a large degree of dispersion, requiring multi-point measurements and reporting of mean and standard deviations. |
| Instrument resolution and probe size | The probe tip radius or beam diameter must be much smaller than the feature size of interest, otherwise the true profile will be smoothed. |
| Specimen preparation (microscopy) | The cutting angle of the section, the quality of the polishing may cause the datum to tilt or interface deformation. |
Operation process
To ensure the comparability and reliability of measurement results, it is recommended to follow the following process:
Pre-characterization: Quantitatively measure the surface roughness parameters of uncoated substrates using a profilometer or atomic force microscope.
Method selection: Choose the appropriate measurement method based on coating transparency, conductivity, allowable failure, and required accuracy.
Calibration and Validation: Method calibration or validation is performed using a standard sample similar to the substrate roughness of the DUT.
Datums are clearly defined: Clearly state the datum model used in the measurement scheme (e.g., midline model or envelope model).
Multi-point system measurement: Perform a sufficient number of replicate measurements in representative areas of the sample.
Data Logging and Reporting: Report the average coating thickness, standard deviation, number of measurement points, and must report both the substrate roughness information and the reference plane definition on which it is based.
Summary
The key to accurate measurement of coating thickness on rough substrates lies in the reasonable definition and consistent determination of the datum. There is no single datum model that is universally applicable to all scenarios, and the selection needs to combine the characteristics of the coating process, performance requirements, and the measurement method itself. The inclusion of matrix roughness parameters as essential accompanying information for thickness measurement reports has become a consensus in the field. In the future, with the advancement of 3D surface topography measurement technology and digital image processing algorithms, the automatic determination of datum and thickness field analysis based on 3D topography data are expected to further improve the accuracy and efficiency of measurement.
References
International Organization for Standardization. Determination of coating thickness of colored paints and varnishes.
American Society for Testing and Materials. Standard test method for measuring the thickness of metal coatings and related coatings by microscopy.
German Standards Institute. Measurement and evaluation of roughness parameters.
A review of surface engineering and coating thickness measurement technology. Transactions of the Chinese Society of Materials Science and Engineering.