Measurement of single-crystal elastic constants by neutron diffraction from polycrystals

1999 ◽  
Vol 32 (4) ◽  
pp. 624-633 ◽  
Author(s):  
C. J. Howard ◽  
E. H. Kisi
Keyword(s):  
Neutron Diffraction ◽  
Single Crystal ◽  
Elastic Constants ◽  
Tetragonal Zirconia ◽  
Uniaxial Stress ◽  
Polycrystalline Materials ◽  
Transformation Toughening ◽  
Reflection Index ◽  
Higher Symmetry ◽  
The Given

The relationships of diffraction averaged elastic compliances for an ideally random polycrystal to the single-crystal elastic compliances are given, within the Reuss approximation, for crystal systems with orthorhombic and higher symmetry. For anisotropic materials, these diffraction elastic compliances are dependent on the reflection indexhkl. Expressions for the conventional elastic constants (Young's modulus, Poisson's ratio) are also given. A connection is made to the `X-ray elastic constants' used for diffraction-based measurements of residual stress. The relationships are used to calculate diffraction averaged constants for comparison with neutron diffraction data recorded from samples under applied uniaxial stress. The Reuss approximation works well for materials with the capacity for plastic deformation, such as metals and transformation toughening ceramics, whereas for other materials the Voigt–Reuss–Hill approximation gives better results. Based on the given relationships and experimental determinations of the diffraction elastic compliances for polycrystalline materials, a method is developed for determining the single-crystal elastic constants. The method for estimating single-crystal compliances is demonstrated here by application to extant data on Ni–Cr–Fe and Ti–6 wt% Al–4 wt% V alloys, and new measurements on cubic zirconia. It has been applied very recently [Kisi & Howard (1998).J. Am. Ceram. Soc.81, 1682–1684] to determine the previously unknown elastic constants for a tetragonal zirconia.

Verification of the elastic constants for α-Al2O3using high-resolution neutron diffraction

2010 ◽  
Vol 44 (1) ◽  
pp. 216-218 ◽  
Author(s):  
Erich H. Kisi ◽  
Christopher J. Howard ◽  
Jianfeng Zhang
Keyword(s):  
High Resolution ◽  
Neutron Diffraction ◽  
Single Crystal ◽  
Elastic Constants ◽  
Diffraction Method ◽  
Polycrystalline Sample ◽  
Lattice Strains ◽  
Recent Suggestion

Precise lattice strains measured using high-resolution neutron diffraction from a solid polycrystalline sample are used to explore the single-crystal elastic constants of α-Al2O3(corundum). The analysis confirms a recent suggestion that, contrary to the long-accepted view, the sign ofs14should be negative. It also indicates that the magnitude ofs13should be adjusted from −0.38 × 10−12to −0.47 × 10−12 Pa−1. It is found that, micromechanically, the polycrystal responds to stress in a manner very close to the Reuss limit. The results confirm the applicability of the diffraction method, which could prove useful when other techniques give ambiguous results.

Residual Stress Measurement of Silicon Nitride and Silicon Carbide by X-Ray Diffraction Using Gaussian Curve Method

1988 ◽  
Vol 32 ◽  
pp. 459-469 ◽  
Author(s):  
Masanori Kurita ◽  
Ikuo Ihara ◽  
Nobuyuki Ono
Keyword(s):  
Residual Stress ◽  
Single Crystal ◽  
Elastic Constants ◽  
Stress Measurement ◽  
Polycrystalline Materials ◽  
X Ray Diffraction ◽  
X Ray ◽  
Small Areas ◽  
Curve Method ◽  
The Continuum

The residual stress induced by grinding or some thermal treatment has a large effect on the strength of ceramics. The X-ray technique can be used to nondestructively measure the residual stress in small areas on the surface of polycrystalline materials. The X-ray stress measurement is based on. the continuum mechanics for macroscopically isotropic polycrystalline materials. In this method, the stress value is calculated selectively from strains of a particular diffraction plane in the grains which are favorably oriented for the diffraction. In general, however, the elastic constants of a single crystal depend on the plane of the lattice, since a single crystal is anisotropic, The behavior of the deformation of individual crystals in the aggregate of polycrystalline materials under applied stress has not yet been solved successfully. Therefore, the stress constant and elastic constants for a particular diffracting plane should be determined experimentally in order to determine the residual stress accurately by X-ray diffraction.

A uniaxial stress apparatus for single-crystal X-ray diffraction on a four-circle diffractometer: application to silicon and diamond

1982 ◽  
Vol 15 (2) ◽  
pp. 148-153 ◽  
Author(s):  
H. d'Armour ◽  
W. Denner ◽  
H. Schulz ◽  
M. Cardona
Keyword(s):  
Single Crystal ◽  
Internal Stress ◽  
Elastic Constants ◽  
Strain Gauge ◽  
Uniaxial Stress ◽  
Unexpected Result ◽  
X Ray Diffraction ◽  
X Ray ◽  
Lattice Constants ◽  
Stress Parameter

An apparatus for applying uniaxial stress to a single-crystal has been constructed. The stress is produced by turning a differential screw and is measured by a strain gauge. The device fits on a goniometer of a four-circle diffractometer and can rotate around all three axes of the goniometer without restrictions. The lattice constants of Si stressed along [111] were measured and compared with ultrasonically measured elastic constants. The internal stress parameter ξ was calculated from changes of the intensity of the 600 reflection: ξ = 0.74 ± 0.04, larger than the value generally accepted (ξ = 0.64 ± 0.04). The implications of this unexpected result are discussed.

Single Crystal Elastic Constants of the MAX Phase Ti3AlC2 Determined by Neutron Diffraction

2010 ◽  
Vol 638-642 ◽  
pp. 2417-2422 ◽  
Author(s):  
Oliver Kirstein ◽  
Jian F. Zhang ◽  
Erich H. Kisi ◽  
D.P. Riley ◽  
M.J. Styles ◽  
...  
Keyword(s):  
Neutron Diffraction ◽  
Single Crystal ◽  
Elastic Constants ◽  
Compressive Load ◽  
Polycrystalline Sample ◽  
Max Phase ◽  
Unit Cell Parameters ◽  
Cell Parameters ◽  
Diffraction Peaks ◽  
Good Agreement

The ternary ceramic Ti3AlC2 has an interesting combination of electrical, thermal and mechanical properties. Single crystal elastic constants under the Reuss approximation for the micromechanical state were obtained by analysing the shifts of neutron diffraction peaks while a polycrystalline sample was subjected to a compressive load varying from 5 to 300 MPa. The values of Young’s modulus and Poisson’s ratio computed from the single crystal compliances are in good agreement with those obtained directly from strain gauges and from the average changes in the a and c unit cell parameters.

scholarly journals Elastic Properties of Polycrystals: A Review

1990 ◽  
Vol 12 (1-3) ◽  
pp. 1-14 ◽  
Author(s):  
S. Hirsekorn
Keyword(s):  
Single Crystal ◽  
Elastic Properties ◽  
Elastic Constants ◽  
Polycrystalline Materials ◽  
Effective Elastic Constants ◽  
Structure Properties

The elastic properties of polycrystals depend on the single-crystal elastic constants of the crystallites which build up the polycrystal and on the manner in which the crystallites are connected. Because of the technical importance of polycrystalline materials a lot of papers deal with the problem to calculate effective elastic constants of polycrystals from single-crystal and structure properties. This paper gives a review concerning the most important theories and methods respecting this matter.

The Ferroelastic Transformation in Yttria- and Ceria-Stabilised Tetragonal Zirconia Via Neutron Diffraction

1994 ◽  
Vol 376 ◽  
Author(s):  
Markys G. Cain ◽  
Mike H. Lewis ◽  
Matthew Backshall ◽  
Stephen M. Bennington ◽  
Steve Hull
Keyword(s):  
Neutron Diffraction ◽  
Direct Evidence ◽  
Tetragonal Zirconia ◽  
Uniaxial Stress ◽  
Preferred Orientation ◽  
X Ray Diffraction ◽  
X Ray ◽  
Stress Criterion ◽  
Energy Absorbing

ABSTRACTNeutron diffraction studies of tetragonal zirconia polycrystals (TZP) subjected to a varying applied uniaxial stress indicates that a ferroelastic crystalline transformation occurs within the bulk of the material. The critical coercive stress was determined to be (1.65±0.03) GPa for yttria stabilised TZP and (0.70±0.05) GPa for ceria stabilised TZP. The results agree well with previous reports concerning the ferroelasticity of tetragonal zirconia, and provide direct evidence indicating that the anomalies observed using the first X-ray diffraction studies originate from the bulk of the ceramic and not solely from the surface. The preferred orientation observed in the tetragonal crystallites was measured as a function of applied uniaxial stress and interpreted via a resolved stress criterion. It is believed that the ferroelastic transformation can act as an energy absorbing mechanism and hence toughen zirconia or ceramics containing dispersed zirconia.

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