Scaling of Average Avalanche Shapes for Acoustic Emission during Jerky Motion of Single Twin Boundary in Single-Crystalline Ni<sub>2</sub>MnGa
Temporal average shapes of crackling noise avalanches, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>U</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo>&l...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Materials |
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| Online Access: | https://www.mdpi.com/1996-1944/16/5/2089 |
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| author | László Z. Tóth Emil Bronstein Lajos Daróczi Doron Shilo Dezső L. Beke |
| author_facet | László Z. Tóth Emil Bronstein Lajos Daróczi Doron Shilo Dezső L. Beke |
| author_sort | László Z. Tóth |
| collection | DOAJ |
| description | Temporal average shapes of crackling noise avalanches, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>U</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>U</mi></semantics></math></inline-formula> is the detected parameter proportional to the interface velocity), have self-similar behavior, and it is expected that by appropriate normalization, they can be scaled together according to a universal scaling function. There are also universal scaling relations between the avalanche parameters (amplitude, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>A</mi></semantics></math></inline-formula>, energy, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>E</mi></semantics></math></inline-formula>, size (area), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>,</mo></mrow></semantics></math></inline-formula> and duration, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>T</mi></semantics></math></inline-formula>), which in the mean field theory (MFT) have the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mo>∝</mo><msup><mi>A</mi><mn>3</mn></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>∝</mo><msup><mi>A</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>∝</mo><msup><mi>T</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula>. Recently, it turned out that normalizing the theoretically predicted average <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>U</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> function at a fixed size, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>U</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><msup><mi>p</mi><mrow><mo>−</mo><mi>b</mi><msup><mi>t</mi><mn>2</mn></msup></mrow></msup></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>a</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>b</mi></semantics></math></inline-formula> are non-universal, material-dependent constants) by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>A</mi></semantics></math></inline-formula> and the rising time, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>R</mi></semantics></math></inline-formula>, a universal function can be obtained for acoustic emission (AE) avalanches emitted during interface motions in martensitic transformations, using the relation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>~</mo><msup><mi>A</mi><mrow><mn>1</mn><mo>−</mo><mi>φ</mi></mrow></msup></mrow></semantics></math></inline-formula> too, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula> is a mechanism-dependent constant. It was shown that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula> also appears in the scaling relations <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mo>~</mo><msup><mi>A</mi><mrow><mn>3</mn><mo>−</mo><mi>φ</mi></mrow></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>~</mo><msup><mi>A</mi><mrow><mn>2</mn><mo>−</mo><mi>φ</mi></mrow></msup></mrow></semantics></math></inline-formula>, in accordance with the enigma for AE, that the above exponents are close to 2 and 1, respectively (in the MFT limit, i.e., with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>φ</mi><mo>=</mo></mrow></semantics></math></inline-formula> 0, they are 3 and 2, respectively). In this paper, we analyze these properties for acoustic emission measurements carried out during the jerky motion of a single twin boundary in a Ni<sub>50</sub>Mn<sub>28.5</sub>Ga<sub>21.5</sub> single crystal during slow compression. We show that calculating from the above-mentioned relations and normalizing the time axis of the average avalanche shapes with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>A</mi><mrow><mn>1</mn><mo>−</mo><mi>φ</mi></mrow></msup></mrow></semantics></math></inline-formula>, and the voltage axis with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>A</mi></semantics></math></inline-formula>, the averaged avalanche shapes for the fixed area are well scaled together for different size ranges. These have similar universal shapes as those obtained for the intermittent motion of austenite/martensite interfaces in two different shape memory alloys. The averaged shapes for a fixed duration, although they could be acceptably scaled together, showed a strong positive asymmetry (the avalanches decelerate much slower than they accelerate) and thus did not show a shape reminiscent of an inverted parabola, predicted by the MFT. For comparison, the above scaling exponents were also calculated from simultaneously measured magnetic emission data. It was obtained that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula> values are in accordance with theoretical predictions going beyond the MFT, but the AE results for <i>φ</i> are characteristically different from these, supporting that the well-known enigma for AE is related to this deviation. |
| first_indexed | 2024-03-11T07:18:34Z |
| format | Article |
| id | doaj.art-6de8afe1f51c43799e9d223db4c5d190 |
| institution | Directory Open Access Journal |
| issn | 1996-1944 |
| language | English |
| last_indexed | 2024-03-11T07:18:34Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Materials |
| spelling | doaj.art-6de8afe1f51c43799e9d223db4c5d1902023-11-17T08:07:08ZengMDPI AGMaterials1996-19442023-03-01165208910.3390/ma16052089Scaling of Average Avalanche Shapes for Acoustic Emission during Jerky Motion of Single Twin Boundary in Single-Crystalline Ni<sub>2</sub>MnGaLászló Z. Tóth0Emil Bronstein1Lajos Daróczi2Doron Shilo3Dezső L. Beke4Department of Solid State Physics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, HungaryFaculty of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa 3200003, IsraelDepartment of Solid State Physics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, HungaryFaculty of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa 3200003, IsraelDepartment of Solid State Physics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, HungaryTemporal average shapes of crackling noise avalanches, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>U</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>U</mi></semantics></math></inline-formula> is the detected parameter proportional to the interface velocity), have self-similar behavior, and it is expected that by appropriate normalization, they can be scaled together according to a universal scaling function. There are also universal scaling relations between the avalanche parameters (amplitude, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>A</mi></semantics></math></inline-formula>, energy, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>E</mi></semantics></math></inline-formula>, size (area), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>,</mo></mrow></semantics></math></inline-formula> and duration, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>T</mi></semantics></math></inline-formula>), which in the mean field theory (MFT) have the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mo>∝</mo><msup><mi>A</mi><mn>3</mn></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>∝</mo><msup><mi>A</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>∝</mo><msup><mi>T</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula>. Recently, it turned out that normalizing the theoretically predicted average <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>U</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> function at a fixed size, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>U</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><msup><mi>p</mi><mrow><mo>−</mo><mi>b</mi><msup><mi>t</mi><mn>2</mn></msup></mrow></msup></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>a</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>b</mi></semantics></math></inline-formula> are non-universal, material-dependent constants) by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>A</mi></semantics></math></inline-formula> and the rising time, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>R</mi></semantics></math></inline-formula>, a universal function can be obtained for acoustic emission (AE) avalanches emitted during interface motions in martensitic transformations, using the relation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>~</mo><msup><mi>A</mi><mrow><mn>1</mn><mo>−</mo><mi>φ</mi></mrow></msup></mrow></semantics></math></inline-formula> too, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula> is a mechanism-dependent constant. It was shown that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula> also appears in the scaling relations <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mo>~</mo><msup><mi>A</mi><mrow><mn>3</mn><mo>−</mo><mi>φ</mi></mrow></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>~</mo><msup><mi>A</mi><mrow><mn>2</mn><mo>−</mo><mi>φ</mi></mrow></msup></mrow></semantics></math></inline-formula>, in accordance with the enigma for AE, that the above exponents are close to 2 and 1, respectively (in the MFT limit, i.e., with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>φ</mi><mo>=</mo></mrow></semantics></math></inline-formula> 0, they are 3 and 2, respectively). In this paper, we analyze these properties for acoustic emission measurements carried out during the jerky motion of a single twin boundary in a Ni<sub>50</sub>Mn<sub>28.5</sub>Ga<sub>21.5</sub> single crystal during slow compression. We show that calculating from the above-mentioned relations and normalizing the time axis of the average avalanche shapes with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>A</mi><mrow><mn>1</mn><mo>−</mo><mi>φ</mi></mrow></msup></mrow></semantics></math></inline-formula>, and the voltage axis with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>A</mi></semantics></math></inline-formula>, the averaged avalanche shapes for the fixed area are well scaled together for different size ranges. These have similar universal shapes as those obtained for the intermittent motion of austenite/martensite interfaces in two different shape memory alloys. The averaged shapes for a fixed duration, although they could be acceptably scaled together, showed a strong positive asymmetry (the avalanches decelerate much slower than they accelerate) and thus did not show a shape reminiscent of an inverted parabola, predicted by the MFT. For comparison, the above scaling exponents were also calculated from simultaneously measured magnetic emission data. It was obtained that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula> values are in accordance with theoretical predictions going beyond the MFT, but the AE results for <i>φ</i> are characteristically different from these, supporting that the well-known enigma for AE is related to this deviation.https://www.mdpi.com/1996-1944/16/5/2089twin boundary motionacoustic and magnetic emissionscaling relationstemporal shapes of avalanches |
| spellingShingle | László Z. Tóth Emil Bronstein Lajos Daróczi Doron Shilo Dezső L. Beke Scaling of Average Avalanche Shapes for Acoustic Emission during Jerky Motion of Single Twin Boundary in Single-Crystalline Ni<sub>2</sub>MnGa Materials twin boundary motion acoustic and magnetic emission scaling relations temporal shapes of avalanches |
| title | Scaling of Average Avalanche Shapes for Acoustic Emission during Jerky Motion of Single Twin Boundary in Single-Crystalline Ni<sub>2</sub>MnGa |
| title_full | Scaling of Average Avalanche Shapes for Acoustic Emission during Jerky Motion of Single Twin Boundary in Single-Crystalline Ni<sub>2</sub>MnGa |
| title_fullStr | Scaling of Average Avalanche Shapes for Acoustic Emission during Jerky Motion of Single Twin Boundary in Single-Crystalline Ni<sub>2</sub>MnGa |
| title_full_unstemmed | Scaling of Average Avalanche Shapes for Acoustic Emission during Jerky Motion of Single Twin Boundary in Single-Crystalline Ni<sub>2</sub>MnGa |
| title_short | Scaling of Average Avalanche Shapes for Acoustic Emission during Jerky Motion of Single Twin Boundary in Single-Crystalline Ni<sub>2</sub>MnGa |
| title_sort | scaling of average avalanche shapes for acoustic emission during jerky motion of single twin boundary in single crystalline ni sub 2 sub mnga |
| topic | twin boundary motion acoustic and magnetic emission scaling relations temporal shapes of avalanches |
| url | https://www.mdpi.com/1996-1944/16/5/2089 |
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