X-ray Diffraction Stress Analysis with Constant Tilt Angle

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Solution Overview

Problem

Conventional X-ray diffraction methods are inefficient and prone to mechanical errors when measuring stress in thin films and coatings, as they require multiple measurements at varying tilt angles, leading to significant sample height errors and prolonged measurement times, especially for low 2θ diffraction cones which are sensitive to noise-induced shifts.

Innovation Solution

A method using a two-dimensional X-ray detector with a constant tilt angle ψ and incremental rotations about the φ axis to perform low 2θ diffraction stress analysis, minimizing sample height errors and reducing the number of measurements needed, allowing for accurate stress tensor characterization with reduced mechanical errors.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If multiple measurements at varying tilt angles are performed, then stress tensor characterization can be achieved, but sample height errors increase and measurement time prolongs

Engineering Contradiction:
Improvestress tensor characterization accuracyVSAvoidmeasurement time
Core Design Contradiction:
Measurement precisionVSLoss of time

Solution Approach 1:

The measurement process is segmented into two independent parts: tilt angle ψ is held constant while φ is varied in discrete steps. This segmentation allows the stress tensor to be characterized by measuring diffraction patterns at multiple φ orientations without changing the tilt angle, thereby avoiding sample height variations while maintaining measurement completeness.

Inventive Principle:
Principle #1Segmentation

Solution Approach 2:

The sample is pre-positioned at a specific tilt angle ψ before beginning the measurement sequence. By establishing this preliminary orientation and maintaining it throughout all measurements, the method eliminates the need for repeated adjustments that would cause sample height errors and time delays.

Inventive Principle:
Principle #10Preliminary action

2Measurement precision

If multiple measurements at varying tilt angles are performed, then stress tensor characterization can be achieved, but mechanical errors increase

Engineering Contradiction:
Improvestress tensor characterization accuracyVSAvoidmechanical error
Core Design Contradiction:
Measurement precisionVSReliability

Solution Approach 1:

The measurement process is segmented into two independent parts: tilt angle ψ is held constant while φ is varied in discrete steps. This segmentation allows the stress tensor to be characterized by measuring diffraction patterns at multiple φ orientations without changing the tilt angle, thereby avoiding sample height variations while maintaining measurement completeness.

Inventive Principle:
Principle #1Segmentation

Solution Approach 2:

The sample is pre-positioned at a specific tilt angle ψ before beginning the measurement sequence. By establishing this preliminary orientation and maintaining it throughout all measurements, the method eliminates the need for repeated adjustments that would cause sample height errors and time delays.

Inventive Principle:
Principle #10Preliminary action

3Measurement precision

If low 2θ diffraction cones are used, then stress measurement sensitivity is improved, but noise-induced shifts increase

Engineering Contradiction:
Improvestress measurement sensitivityVSAvoidnoise-induced shifts
Core Design Contradiction:
Measurement precisionVSObject-affected harmful factors

Solution Approach 1:

Multiple measurements at different φ orientations are merged into a single comprehensive stress tensor characterization. By combining the information from these repeated measurements while maintaining constant tilt angle, the method enhances sensitivity through multiple data points while avoiding the noise issues that would arise from varying tilt angles.

Inventive Principle:
Principle #5Merging (Combining)

Solution Approach 2:

The method uses feedback from multiple φ-oriented measurements to characterize the stress tensor components. By analyzing the diffraction patterns at different φ angles and comparing them against each other, the system can distinguish true stress-induced shifts from noise, improving measurement reliability.

Inventive Principle:
Principle #23Feedback

4Measurement precision

If conventional X-ray diffraction methods are used, then stress measurement can be performed, but measurement efficiency is reduced

Engineering Contradiction:
Improvestress measurement capabilityVSAvoidmeasurement efficiency
Core Design Contradiction:
Measurement precisionVSProductivity

Solution Approach 1:

The measurement process maintains continuous useful action by keeping the sample at a fixed tilt angle and systematically varying only the φ orientation. This continuous measurement approach at constant ψ eliminates the interruptions and adjustments required by conventional methods, significantly improving measurement efficiency while maintaining stress analysis capability.

Inventive Principle:
Principle #20Continuity of useful action

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

This approach enables precise and rapid measurement of stress tensors in thin films and coatings by maintaining a constant tilt angle during data collection, minimizing sample height variations and noise-induced shifts, thus improving measurement accuracy and reducing the time required for data acquisition.

Implementation Method 1

radiation with a wavelength λ in the subnanometer range is directed to a sample of a crystalline material with a given interatomic spacing, d. When the angle of incidence, θ, relative to the crystalline structure satisfies the Bragg equation, λ = 2d sin θ, an interferometrically reinforced signal (the diffracted signal), may be observed leaving the material

Methodology Applied
Scientific EffectX-ray diffraction: Bragg Diffraction

Data Source

PatentEP3425378B1X-ray diffraction device and method to measure stress with 2d detector and single sample tilt
Publication Date: 2019.12.25 BRUKER AXS INC
  • EP3425378B1 patent drawingFigure 1~2
  • EP3425378B1 patent drawingFigure 3~4
  • EP3425378B1 patent drawingFigure 5~6

AI summary

A method is provided for performing an X-ray diffraction stress analysis of a sample such as a thin film, a coating, or a polymer. The sample has a surface with two perpendicular axes S 1, S 2 within a plane of the surface, and a third axis S 3 perpendicular to the sample surface plane. An X-ray beam is directed at the sample surface at a relatively low angle with regard to the surface plane. X-ray energy is diffracted from the sample and detected with a two-dimensional X-ray detector (108) at a plurality of rotational orientations (Φ) of the sample about S 3. The third axis S 3 is maintained at a constant tilt angle (ψ) during the entire X-ray diffraction stress analysis, thereby avoiding the significant error associated to the movement of a cradle track of a goniometer (100) used for the X-ray diffraction stress analysis and on which measurements at a low 2θ angle are highly sensitive.