DE19719473A1 - Method for non=destructive determination by X-ray diffraction of expansion free grating parameters and/or mechanical stress conditions - Google Patents

Abstract

The method involves the separate determination of the depth distributions of the expansion free grating and stress conditions using the whole diffraction spectrum. To determine the depth profile the Bragg angle qy*,f* for several diffraction maxima is measured in the expansion free direction with Y*, F* for a plane stress condition given by :- with F* optional,V an elastic constant and s11/s22 ratio of stress components. To determine the stress condition at 1/e-penetration depth T the Bragg angle q for the diffraction maxima of severAl reflections is measured. To each reflection there is allocated a tilt angle Y so that the depth T remains constant during the measurement and the stress condition for the penetration depth is given by :- where:- s1 and s2 are x-ray graphical elastic constants for each reflex (hkl)sij:=stress components. To determine depth profiles of the mechanical stress the stress in various I/e penetration depths t is determined

Description

The invention relates to a method for X-ray diffractometric, destroy tion-free determination of strain-free lattice parameters and / or mechani stress states in surface layers of polycrystalline test specimens a gradient of the mechanical stresses and / or the strain-free git have terparameters perpendicular to the test specimen surface.

X-ray diffractometric methods of the type mentioned above are in particular especially for the qualitative assessment of manufacturing, processing and bean stress processes in polycrystalline workpieces, components and products reversible. In particular, load voltage profiles in polycrystalline test specimens can be determined as a result of mechanical-thermal loads in techni constructions or using special load devices  be fathered. In addition to the determination of mechanical stress profiles Lattice parameters in polycrystalline materials also in a non-destructive way and their gradients are examined in surface layers, which change or especially by coating, etching or doping processes can be influenced due to diffusion and corrosion processes. In particular especially for the analysis of general physical surface properties parameters the knowledge of lattice parameters is an important property characteristic polycrystalline materials.

However, a superposition of atypical ones often occurs in polycrystalline materials Tension states, especially tensions with strong vertical gradients to the layer level and gradients of lattice parameters, so that the me chanical stress state also causes crystal lattice distortion. Such overlaps occur particularly when there is friction, wear or chip corrosion cracking, which needs to be recorded qualitatively without examining it to irreversibly impair the test specimen.

The so-called X-ray voltage measurement (RSM) is known X-ray diffractometric method for the determination of load and residual stress conditions in near-surface material areas. In this well-known span voltage measurement it is assumed that the in a crystalline body brought mechanical stresses to a distortion of the elementary cells of the Lead crystal lattice. Expression of this crystal lattice distortion is a relative change tion of the network plane distances Δd / d in the crystal lattice, that of a macroscopic Elongation ε is equated. Such network plane spacing changes X-ray diffractometrically from the change in position of a diffraction maximum Reflexes Δθ, where θ represents the Bragg angle, determines why X-ray diffraction metric recordings of the same reflex from different directions (Φ, Ψ). The following is used to determine the state of elongation ε Relationship used

The same applies to a coupling between strains and stresses in polycrystalline materials under the premise of linear elastic material behavior Use of X-ray elastic constants (s₁, ½ s₂):

In the above relationship, for example, σ₃₃ means the voltage component which shows normal in the direction of the samples and includes the angle (Ψ) with the measuring direction. See also Fig. 1 in which the related Winkelbe references are drawn. According to FIG. 1, there is a sample in the coordinate origin, the sample surface of which lies parallel to the X1-X2 plane. The angle (Φ) used in the above given relationship, on the other hand, spans between (σ₁₁) and the projection of the measuring direction onto the sample plane. The measurement values required for determining the individual voltage components are obtained by correspondingly varying the measuring direction (Φ, Ψ). From the experimental side, a number of measurement and evaluation variants are available in order - depending on the circumstances and requirements - to determine individual or all of the voltage components listed in the above equation.

Assuming a level stress state in the area under investigation of the sample or the test specimen, certain (Φ, Ψ) measuring directions become so-called non-stretching directions in which the crystal lattice spacings d _{Φ , Ψ} assume the size d₀ that is undistorted, ie stress-free Crystal lattice would be measured. If there is a homogeneous voltage and material state in the examination area of the test specimen, this strain-free crystal lattice spacing d₀ can be determined in this way.

Access to all materials with crystalline or semi-crystalline structures or Structural parts explain the wide range of possible applications of RSM. A summary is in "Haug, V., Macherauch, E." advanced in X- Ray analizes ", 1984, No. 27, pages 81 to 99.

A change in the tilt angle (Ψ) necessary for voltage determination, see also FIG. 1, from measurement point to measurement point leads to a variation in the mean penetration depth (τ) of the X-rays within a series of measurements. Basically, two different measurement geometries can be used to vary the tilt angle (Ψ), the so-called Ω geometry and the so-called Ψ geometry. When using the Ω geometries, the mean penetration depth (τ) is determined by the following formula:

However, the following formula is used for measurements according to the Ψ geometry turns:

According to FIG. 2a, in the Ω geometry the tilt axis for setting the Ψ angle corresponds to the center axis of the diffractometer measuring circle, while the tilt axis in Ψ geometry according to FIG. 2b lies in the measuring circle plane of the diffractometer and affects the sample surface. In the above relationships, µ corresponds to the linear attenuation coefficient.

If there are voltage gradients close to the surface, evaluation methods presuppose a constant state of tension over the depth of the measuring area  erroneous results. In known and invarian over the depth of the Meßarials These strain-free lattice parameters (d₀) can numerically correct these errors be eliminated or eliminated by special measuring methods (see Ballard et. al., "Depth profiling biaxial stresses in sputter deposited molybdenum films, use of the cos²Φ-method ", Advanced in X-Ray analysis 39, 1996) but in the case of simultaneous occurrence of stress gradients and gradients of the lattice para meters only depth profiles using X-ray diffractometric methods exclusively can be determined in the streaked beam incidence. However, the disadvantage of this method is that the penetration depth range measurable under grazing beam incidence is about an order of magnitude less than that using conventional X-rays diffractometry would be available.

The invention has for its object a method for X-ray diffractometry non-destructive determination of strain-free lattice parameters and / or mechanical stress states in surface layers polycrystalline ner test specimens that have a gradient of mechanical stress and / or deh have free grid parameters perpendicular to the surface of the test object, such to further develop the depths of penetration to determine depth profiles of chip and grid parameters should be increased significantly.

The solution to the problem on which the invention is based is in claim 1 specified. Features that extend the concept of the invention are the subject matter of subclaims.

According to the invention, the method according to the preamble of claim 1 provides that for the separate determination of depth distributions of the strain-free lattice pair rameter and the state of tension, the information of the entire diffracto metric diffraction spectrum can be used. The inventive method ren is divided into two process stages, a first experiment to determine the Profile of the strain-free lattice parameters and a second experiment to span measurement at different depths of the sample.  

In the first step, the line position of several diffraction maxima in strain-free directions is determined to determine the depth profile of the strain-free grating parameters. To determine an expansion-free direction Ψ *, the relationship described above for ε _{( Φ , Ψ )} is first set to zero. With this determination equation, the strain-free direction Ψ *, which can be solved under the boundary condition of a flat stress state, can be determined. Ψ * can also be taken, for example, using a method described by Haug (see VM Haug et al., Med. Trans. A. 13 A, 1239, 1992). The following relationship is determined for Ψ *:

The parameter ν stands for an elastic material constant, whereby the tension ratio σ₁₁ / σ₂₂ can be determined without knowledge of the lattice parameters.

The first one is simplified for a rotationally symmetrical stress state equation

Under the tilt angle Ψ * the grating parameter d₀ (Ψ *) is known for all suitable reflexes. The penetration depth of the X-rays varies according to the formulas

using the Ω geometry or Ψ geometry described above with the Bragg angle Θ. In this way, a profile d₀ (τ) can be obtained from the measurements. created and stored numerically.

In the second experiment, the voltage measurements are made with the known one sin²Ψ method performed at various predetermined depth levels τ. The  The tilt angles Ψ (Θ, τ) to be set for the individual reflections result from standing equations for the Ω geometry using an Ω Diffractometer too

A corresponding tilt angle relationship using a Ψ- Diffratometers results

Essential for determining the state of stress at a certain penetration depth τ is that the Bragg angle Θ of the diffraction maxima of several reflections is measured. Each reflex is assigned a tilt angle Ψ in this way becomes that the predetermined depth of penetration τ remains constant during the measurement. Of the The stress state is subsequently determined using conventional methods, e.g. B. after sin²Ψ method determined. The following relationship applies:

The invention is described below with reference to the figures without limitation kung the general inventive concept based on an embodiment wrote. Show it:

Fig. 1 sample and angular geometry röntgendiffratometrischer investigations,

Fig. 2 angular relationships in the Ω-geometry and Ψ-Geoemtrie,

Fig. 3 table for X-ray stress analysis of Ti (CN),

Fig. 4 diagram of a depth profile of the lattice constants

Fig. 5 table for tilt angle for voltage measurement,

Fig. 6 sin²Ψ Chart 3 microns in depth,

Fig. 7 table with measurement results for voltage values and penetration depth, as well

Fig. 8 voltage depth profile measurement.

As already described above, FIGS . 1 and 2 show basic geometry representations for X-ray examination methods, to which reference is only made at this point.

In a contribution by B. Eigenmann and Macherauch, E. Mat.-wiss u. Materials technology nik 26, 199-216, 1995, are elastic constants and non-stretching directions for individual reflections during a voltage measurement on Ti (C, N) were put together those obtained by measurements using an Ω diffractometer were.

The measurements are carried out on a 5 μm thick Ti (C, N) gradient layer which has not been reactively sputtered onto a WC / Co-Targett. The state of stress in the layer can be regarded as rotationally symmetrical. The linear attenuation coefficient for Cu-Kα radiation is µ = 0.0826 µm ^-1 and can be assumed to be constant over the depth of the measurement area.

Among those in the table of FIG 3 tilt angles Ψ listed * the associated reflections {hkl} were measured and calculated in known manner by means of the Bragg equation, the lattice parameter d₀.. Then with the help of

for the cubically crystallizing Ti (C, N) the d₀ values are converted into the lattice constant a₀ calculates.

In FIG. 4, the lattice constant of the weighted average is 1 / e penetration depth of X-rays applied τ. A back calculation to the sample depth z according to

gives a linear profile p (z) for the lattice constant of the form

The stress measurements were made for penetration depths τ between 1 µm and 4.5 µm carried out. The associated tilt angles were made accordingly

determined and are shown in the table in FIG. 5.

Diagrams were recorded for all penetration depths using the sin²Ψ method of X-ray stress measurement and the residual stresses were determined. An example of such a sin²Ψ diagram is shown in FIG. 6.

The associated measurement results are listed in the table in accordance with FIG. 7 and shown in FIG. 8 as a stress depth profile. The weighted mean 1 / e penetration depth τ was used as the abscissa parameter.

Claims (5)

1.Procedure for the X-ray diffractometric, non-destructive determination of strain-free lattice parameters and / or mechanical stress states in surface layers of polycrystalline test specimens which have a gradient of the mechanical stresses and / or the strain-free lattice parameters perpendicular to the test specimen surface, characterized by separate determination of depth distributions of the strain-free lattice parameters and the stress state using the entire diffractometric diffraction spectrum in such a way

• - That to determine the depth profile of the strain-free grating parameters, the Bragg angle θ _{Ψ *, Φ *} of several diffraction maxima is measured in strain-free directions Ψ *, Φ *, where Ψ *, Φ * stood for a flat stress condition with Φ * any
  ν elastic constant and
  σ₁₁ / σ₂₂ ratio of stress components
  are given and for each measured Bragg angle the lattice parameter is determined, to which a 1 / e penetration depth T is assigned by means of diffractometric measurement,
• - That the Bragg angle θ of the diffraction maxima of several reflections is measured to determine the voltage state in a certain 1 / e penetration depth T, each tilt being assigned a tilt angle Ψ such that the predetermined 1 / e penetration depth T is constant during the measurement remains, and the stress state ε for the given 1 / e penetration depth τ with tels with s1 and s2 X-ray elastic constants for each reflex (hkl) σ _ÿ : = stress components
  is determined and, in order to determine a depth profile of the mechanical stress, the stress determination is carried out in different 1 / e penetration depths τ.

2. The method according to claim 1, characterized in that the diffractometric measurement for determining the 1 / e penetration depth T for the assignment to the lattice parameters by means of a Ψ diffractometer takes place using the following relationship: 3. The method according to claim 1, characterized in that the diffractometric measurement for determining the 1 / e penetration depth τ for the assignment to the lattice parameters by means of an Ω diffractometer takes place using the following relationship: 4. The method according to any one of claims 1 to 3, characterized in that the assignment of the tilt angle Ψ to each reflex when determining the voltage state with the aid of a Ψ diffractometer, he uses the following relationship: with µ: = mass weakening coefficient. 5. The method according to any one of claims 1 to 3, characterized in that the assignment of the tilt angle Ψ to each reflex when determining the voltage state with the aid of an Ω diffractometer he uses the following relationship: with µ: = mass weakening coefficient.