Predicting multipulse laser-induced failure for molybdenum metal mirrors

Michael F. Becker; Chunchi Ma; Rodger M. Walser

doi:10.1364/AO.30.005239

Applied Optics
Vol. 30,
Issue 36,
pp. 5239-5246
(1991)
•https://doi.org/10.1364/AO.30.005239

Predicting multipulse laser-induced failure for molybdenum metal mirrors

Michael F. Becker, Chunchi Ma, and Rodger M. Walser

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Michael F. Becker, Chunchi Ma, and Rodger M. Walser, "Predicting multipulse laser-induced failure for molybdenum metal mirrors," Appl. Opt. 30, 5239-5246 (1991)

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Abstract

In combination with known thermomechanical-fatigue data for Mo, we have conducted transient photothermal deflection (TPD) measurements to develop a model for the multipulse laser damage of Mo mirrors to predict their lifetimes. In laser-damage experiments to verify the model, Mo mirrors were irradiated with 10-ns Nd:YAG laser pulses at 1064 nm at a 10-Hz repetition rate. Digitized TPD waveforms indicated peak surface angular deflection that could then be converted into surface displacement. Numerical modeling of the vertical heat distribution enabled the peak surface-deflection signal to be converted into peak surface temperature. The thermomechanical model was verified by both the experimental and the numerical results. Conventional mechanical-fatigue data for Mo were used to derive a predictive equation for the laser-accumulation lifetime of Mo mirrors. Experiments were performed with 1–10⁴ pulses per site, yielding laser-damage thresholds and accumulation curves. The accumulation behavior predicted from measurements of mechanical fatigue was in excellent agreement with the measured behavior. Thus a single-pulse TPD measurement of peak deformation at a subthreshold laser fluence, in conjunction with mechanical-fatigue data, may be used to estimate the safe operating fluence for a component in a multipulse laser environment.

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Symbol	Name	Value	Units	Source Reference
ΔT	Temperature difference	T − 300 K	K	Definition
R	Reflectance	0.67	None	Measured at 1 μm
A	Absorptance	0.33 + 2 × 10⁻⁵ ΔT	None	From R and 14
T_m	Melt temperature	2883	K	15
ρ	Density	10.22	g/cm³	15
C_υ	Specific heat	0.276 + 4.35 × 10⁻⁸ ΔT²	J/gK	15
k_th	Thermal condition	1.40 − 4.0 × 10⁻⁴ ΔT, T < 2150 K	W/cm K	15
k_th	Thermal condition	0.68; T > 2150 K	W/cm K	15
α	Thermal expansion coefficient	5.0 × 10⁻⁶ + 1.25 × 10⁻⁹ ΔT	K⁻¹	15
ν	Poisson's ratio	0.32	None	15
E	Young's modulus	325	GPa	15
Y	0.01% Yield stress	0.35, T = 300 K	GPa	15
		0.30, T = 350 K	GPa	15
		0.23, T = 450 K	GPa	15

Type of Experiment	N	Temperature (K)	Exponent	s	Reference	Notes
Controlled strain	< 6 × 10⁴	300	c = −0.33	0.87	10	Plastic strain computed
Controlled strain	< 10²	300	c = −0.39	0.88	11	Total strain uncorrected
Controlled strain	< 10²	973	c = −0.39	0.88	11	Total strain uncorrected
Controlled strain	< 10²	1273	c = −0.39	0.88	11	Total strain uncorrected
Controlled stress	10⁴ – 10⁵	300	b = −0.098	0.90	12	Stress given
Controlled strain	< 10⁴	300	c = −0.58	0.92	13	Plastic strain given
Controlled strain	< 10⁴	773	c = −0.34	0.87	13	Plastic strain given
Controlled strain	< 10⁴	1073	c = −0.32	0.86	13	Plastic strain given
Average		300		0.88 (±0.01)

Symbol	Name	Value	Units	Source Reference
ΔT	Temperature difference	T − 300 K	K	Definition
R	Reflectance	0.67	None	Measured at 1 μm
A	Absorptance	0.33 + 2 × 10⁻⁵ ΔT	None	From R and 14
T_m	Melt temperature	2883	K	15
ρ	Density	10.22	g/cm³	15
C_υ	Specific heat	0.276 + 4.35 × 10⁻⁸ ΔT²	J/gK	15
k_th	Thermal condition	1.40 − 4.0 × 10⁻⁴ ΔT, T < 2150 K	W/cm K	15
k_th	Thermal condition	0.68; T > 2150 K	W/cm K	15
α	Thermal expansion coefficient	5.0 × 10⁻⁶ + 1.25 × 10⁻⁹ ΔT	K⁻¹	15
ν	Poisson's ratio	0.32	None	15
E	Young's modulus	325	GPa	15
Y	0.01% Yield stress	0.35, T = 300 K	GPa	15
		0.30, T = 350 K	GPa	15
		0.23, T = 450 K	GPa	15

Type of Experiment	N	Temperature (K)	Exponent	s	Reference	Notes
Controlled strain	< 6 × 10⁴	300	c = −0.33	0.87	10	Plastic strain computed
Controlled strain	< 10²	300	c = −0.39	0.88	11	Total strain uncorrected
Controlled strain	< 10²	973	c = −0.39	0.88	11	Total strain uncorrected
Controlled strain	< 10²	1273	c = −0.39	0.88	11	Total strain uncorrected
Controlled stress	10⁴ – 10⁵	300	b = −0.098	0.90	12	Stress given
Controlled strain	< 10⁴	300	c = −0.58	0.92	13	Plastic strain given
Controlled strain	< 10⁴	773	c = −0.34	0.87	13	Plastic strain given
Controlled strain	< 10⁴	1073	c = −0.32	0.86	13	Plastic strain given
Average		300		0.88 (±0.01)

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Equations (10)

Applied Optics