### Abstract

Photothermal laser beam deflection (PTD) is a powerful tool used to obtain the thermal diffusivities of bulk solids and thin films. PTD is of special interest for non-destructuve evaluation of bulk, thin film and composite materials anticipated for use in future space missions. Polycrystalline diamond thin films are expected to be useful as heat sinks and thermal conductors in space applications, and measurement of thermal diffusivity in these films is very important. One of the major problems in applying the PTD technique for diffusivity measurements (and hence the thermal conductivity, since heat capacities and densities are not difficult to measure and are frequently known) is that a numerical regression analysis must be performed to simultaneously determine several unknown parameters. Regression is done by matching experimental data with calculations based on analytic models such that an error function is minimized. This paper describes the adaption of the Levenberg-Marquardt algorithm for regression analysis to the determination of thermal diffusivity of bulk and thin film solids by PTD. The analytic theory is reviewd and the numerical analysis method is described. Experimental equipment for high signal-to-noise ratio data is described and data on bulk aluminum taken over a range of frequencies are presented. Regression analysis fits to the theory (performed in an inverse space reference frame) yield values for parameters of the experiment, including the thermal diffusivity.

Original language | English (US) |
---|---|

Pages (from-to) | 103-107 |

Number of pages | 5 |

Journal | Thin Solid Films |

Volume | 215 |

Issue number | 1 |

DOIs | |

State | Published - Jul 30 1992 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Surfaces and Interfaces
- Surfaces, Coatings and Films
- Metals and Alloys
- Materials Chemistry

### Cite this

*Thin Solid Films*,

*215*(1), 103-107. https://doi.org/10.1016/0040-6090(92)90709-K

**Thermal diffusivity measurements by photothermal laser beam deflection (PTD) : data analysis using the Levenberg-Marquardt algorithm.** / Machlab, Hassanayn; McGahan, William A.; Woollam, John A.

Research output: Contribution to journal › Article

*Thin Solid Films*, vol. 215, no. 1, pp. 103-107. https://doi.org/10.1016/0040-6090(92)90709-K

}

TY - JOUR

T1 - Thermal diffusivity measurements by photothermal laser beam deflection (PTD)

T2 - data analysis using the Levenberg-Marquardt algorithm

AU - Machlab, Hassanayn

AU - McGahan, William A.

AU - Woollam, John A.

PY - 1992/7/30

Y1 - 1992/7/30

N2 - Photothermal laser beam deflection (PTD) is a powerful tool used to obtain the thermal diffusivities of bulk solids and thin films. PTD is of special interest for non-destructuve evaluation of bulk, thin film and composite materials anticipated for use in future space missions. Polycrystalline diamond thin films are expected to be useful as heat sinks and thermal conductors in space applications, and measurement of thermal diffusivity in these films is very important. One of the major problems in applying the PTD technique for diffusivity measurements (and hence the thermal conductivity, since heat capacities and densities are not difficult to measure and are frequently known) is that a numerical regression analysis must be performed to simultaneously determine several unknown parameters. Regression is done by matching experimental data with calculations based on analytic models such that an error function is minimized. This paper describes the adaption of the Levenberg-Marquardt algorithm for regression analysis to the determination of thermal diffusivity of bulk and thin film solids by PTD. The analytic theory is reviewd and the numerical analysis method is described. Experimental equipment for high signal-to-noise ratio data is described and data on bulk aluminum taken over a range of frequencies are presented. Regression analysis fits to the theory (performed in an inverse space reference frame) yield values for parameters of the experiment, including the thermal diffusivity.

AB - Photothermal laser beam deflection (PTD) is a powerful tool used to obtain the thermal diffusivities of bulk solids and thin films. PTD is of special interest for non-destructuve evaluation of bulk, thin film and composite materials anticipated for use in future space missions. Polycrystalline diamond thin films are expected to be useful as heat sinks and thermal conductors in space applications, and measurement of thermal diffusivity in these films is very important. One of the major problems in applying the PTD technique for diffusivity measurements (and hence the thermal conductivity, since heat capacities and densities are not difficult to measure and are frequently known) is that a numerical regression analysis must be performed to simultaneously determine several unknown parameters. Regression is done by matching experimental data with calculations based on analytic models such that an error function is minimized. This paper describes the adaption of the Levenberg-Marquardt algorithm for regression analysis to the determination of thermal diffusivity of bulk and thin film solids by PTD. The analytic theory is reviewd and the numerical analysis method is described. Experimental equipment for high signal-to-noise ratio data is described and data on bulk aluminum taken over a range of frequencies are presented. Regression analysis fits to the theory (performed in an inverse space reference frame) yield values for parameters of the experiment, including the thermal diffusivity.

UR - http://www.scopus.com/inward/record.url?scp=0026895571&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026895571&partnerID=8YFLogxK

U2 - 10.1016/0040-6090(92)90709-K

DO - 10.1016/0040-6090(92)90709-K

M3 - Article

AN - SCOPUS:0026895571

VL - 215

SP - 103

EP - 107

JO - Thin Solid Films

JF - Thin Solid Films

SN - 0040-6090

IS - 1

ER -