**Publications**(41)

This will count as one of your downloads.

You will have access to both the presentation and article (if available).

_{C}--i.e., the effective strength of a uniformly stressed 1-cm

^{2}area---and the shape parameter

*m*, which reflects the dispersion of surface-flaw sizes. A statistical analysis of flexural strength data thus amounts to obtaining the parameters σ

_{C}and

*m*, which is best done by directly fitting estimated cumulative failure probabilities to the appropriate expression derived from Weibull's theory. In this light, we demonstrate that (a) at the 1% failure-probability level, fusion-cast CaF

_{2}and OxyFluoride Glass perform poorly compared to CVD-ZnSe; (b) available data for fused SiO

_{2}and sapphire confirm the area-scaling principle, thus validating Weibull's theory; and (c) compressive coatings enhance the characteristic strength but degrade the shape parameter, which mitigates their benefit. In Appendix, it is shown that four-point bending data for fusion-cast CaF

_{2}do not obey a simple two-parameter model but are indicative of a bimodal surface-flaw population.

_{2}). The strength of this material is known to be highly dependent on the stressed area and the surface finish, but has not yet been properly characterized in the published literature. Recently, Detrio and collaborators at the University of Dayton Research Institute (UDRI) performed extensive ring-on-ring flexural strength measurements on fused Si0

_{2}specimens ranging in size from 1 to 9 inches in diameter and of widely differing surface quality. In this contribution, we report on a Weibull statistical analysis of the UDRI data-an analysis based on the procedure outlined in

*Proc. SPIE*4375, 241 (2001). We demonstrate that: (a) a two-parameter Weibull model, including the area-scaling principle, applies; (b) the shape parameter (m is asymptotically equal to 10) is essentially independent of the stressed area as well

*as*the surface finish; (c) the characteristic strength (1-cm2 uniformly stressed area) obeys a linear law, σ

_{C}(in MPa) is asymptotically equal to 160 - 2.83x PBS®(in ppm/sr), where PBS® measures the surface/subsurface "damage." In this light, we evaluate the cumulative failure probability of optically polished and superpolished fused Si0

_{2}windows as a function of the biaxial tensile stress, for uniformly stressed areas ranging from 0.3 to 100 cm

^{2}.

^{TM}) - has been promoted as an ideal solution of the Airborne Laser (ABL) window problem in the sense that it will allow obtaining large "athermal" windows for high-energy lasers (HEL) operating at the chemical oxygen-iodine laser (COIL) wavelength [K. Billman,

*et al.*, Proc. SPIE

**5647**, 207 (2005)]. In this context, we emphazise that the performance of a laser-window material candidate must be assessed not only in terms of its ability to transmit high-power beams without generating undue optical distortion but also in terms of the constraints imposed by stress-related failure modes. Here, we provide the tools to carry out an analysis of both pressure- and beam-induced stresses, in addition to thermally induced aberrations, and illustrate the procedure through model windows made of (111)-oriented CaF

_{2}, fusion-cast CaF

_{2}, and OFG

^{TM}glass. Regarding OFG, we find that (a) this material will be vulnerable to surface compressive stresses on account of its poor thermal conductivity; (b) the stress-birefringence contribution to optical distortions cannot be ignored, which rules out creating a zero-distortion ABL window; and (c) based on Strehl ratios, and in the absence of stress-driven failure modes, OFG outperforms Si0

_{2}but does not match the performance of fusion-cast CaF

_{2}. Regarding CaF

_{2}, we find that (a) fusion-cast CaF

_{2}exhibits substantial stress-induced birefringence, which prohibits using this material if depolarization is an issue; (b) highly-oriented (111)CaF

_{2}exhibits no stress-birefringence at the COIL wavelength, in accord with previous investigations at HF/DF frequencies; and (c) in principle, (111) CaF

_{2}windows may transmit aberration-free beam fluences in the 1-MJ/cm

^{2}range but will require improvements in strength to achieve reliable designs.

_{2}, which we do here on the basis of available (Dec '04) property data for fusion-cast CaF

_{2}and OFG. Oxyfloride glass was found to be deficient in regard to thermal diffusivity, which may lead to excessive coating-induced compressive stresses, and stress- birefringence, which rules out creating a distortion-free window. It is suggested that future efforts should be directed at strengthening CaF

_{2}in view of this material's exceptionally low absorbtion and almost no stress-birefringence

_{N})+mln((sigma) ), where P is the cumulative failure probability, (sigma) is the applied tensile stress, m is the Weibull modulus, and (sigma)

_{N}is the nominal strength. The strength of (sigma)

_{N}, however, does not represent a true measure because it depends not only on the test method but also on the size of the volume or the surface subjected to tensile stresses. In this paper we intend to first clarify issues relating to the application of Weibull's theory of fracture and then make use of the theory to assess the results of equibiaxial flexure testing that was carried out on polycrystalline infrared-transmitting materials. These materials are brittle ceramics, which most frequently fail as a consequence of tensile stresses acting on surface flaws. Since equibiaxial flexure testing is the preferred method of measuring the strength of optical ceramics, we propose to formulate the failure-probability equation in terms of a characteristic strength, (sigma)

_{C}, for biaxial loadings, i.e., P=1-exp{-(pi) (r

_{o}/cm)

^{2}[(Gamma) (1+1/m)]

^{m}((sigma) /(sigma)

_{C})

^{m}}, where r

_{o}is the radius of the loading ring (in centimeter) and (Gamma) (z) designates the gamma function. A Weibull statistical analysis of equibiaxial strength data thus amounts to obtaining the parameters m and (sigma)

_{C}, which is best done by directly fitting estimated P

_{i}vs i data to the failure-probability equation; this procedure avoids distorting the distribution through logarithmic linearization and can be implemented by performing a non-linear bivariate regression. Concentric- ring fracture testing performed on five sets of Raytran materials validates the procedure in the sense that the two parameters model appears to describe the experimental failure-probability distributions remarkably well. Specifically, we demonstrate that the wide divergence in published CVD-diamond strength data reflects the poor Weibull modulus of this material and must be attributed to the size effect rather than the quality of the deposits. Finally, the problem of obtaining correct failure stresses from the measured failure loads is examined in the Appendix.

_{Bi greater than 1}equals R

_{H}, i.e., the Hasselman parameter for strong shocks; in a thermally thin regime, however, the appropriate figure of merit is (FoM)

_{Bi less than 1}equals sigma

_{f}

^{n}R'

_{H}with n equals 1/2 for flat plates and n equals 2/3 for hemispherical shells, and not the Hasselman parameter R'

_{H}for mild shocks. Judging from the results of thermal shock testing performed elsewhere, we conclude that in a laminar flow environment the allowable heat flux on a thermally thin IR dome can be expressed as follows: Q

_{lim}equals 2R'

_{H}/L, where L is the dome thickness. This expression provides a direct means of obtaining the Mach altitude failure line for a dome of given thickness and given radius, if the initial wall temperature is known. Furthermore, it then becomes straightforward to assess the thermal shock resistance capability of a thickness-optimized IR dome either in terms of the allowable heat load or, more simply, the allowable stagnation temperature.

_{DB}) exhibits a spot size (2(omega) ) dependence best described as follows: E

_{DB}equals A(root)2(omega) with A approximately equals 24 MV(root)micrometers /cm in the visible and A approximately equals 48 MV(root)micrometers /cm in the infrared. This demostrates that the optical strength of diamond is comparable to the strength of well established wide-bandgap laser-windows material candidates.

_{eff}/NEI, where H

_{eff}represents an effective target irradiance and NEI is the system's noise-equivalent irradiance at the peak-response wavelength of the detector. The NEI characterizes the capability of the system and is best expressed in terms of a `dark-system NEI,' which refers to the noise-equivalent irradiance in a laboratory environment, and a `photon noise factor' that relates noise originating from the background scene, the infrared window, and the detector surroundings to the photon noise of a dark system. A set of equations is derived for evaluating the performance degradation resulting from the photon exitance of the `hot window,' taking into account the effect of radiation- shielding procedures. The missile window problem is then formulated in a general but compact form compatible with the state of the art of IR technology. An illustration is provided in the context of assessing the feasibility of using pyramidal domes for dual-mode air-to-air missile applications; it is shown how to evaluate the IR performance degradation induced by aerodynamic heating of such domes under conditions that are representative of anticipated thermally most severe trajectories for internal as well as external missile-carry configurations.

_{BD}) at the damage threshold of diamond obeys a pattern best described as follows: E

_{BD}approximately equals A/(root)2(omega) , where A equals 30.7 and 38.7 MV(mu)

^{1/2}/cm at 532 and 1064 nm, respectively. The case of CVD diamond demonstrates that, if problems arising from localized high absorption at the deposition surface can be avoided, this material should be of much promise for contemplated high-power free-electron laser window applications. We show that corrections for self- focusing in laser damage experiments depend not only on the peak pulse power but also on the position of the diffraction prefocus and the length of the Rayleigh range.

_{11}equals 1050 GPa, which assumes that is does not vary much with orientation, and many authors use (upsilon) equals 0.2 as an appropriate average value of Poisson's ratio, which is incorrect. In fact, since the elastic constants of diamond are known with great accuracy, it is a straightforward matter to derive exact numbers for E and (upsilon) that take into consideration the stress direction, the intrinsic anisotropy, as well as the crystalline configuration. For CVD diamond deposits, we find that, in a first approximation, the Hershey-Kroner-Eshelby averaging procedures yields acceptable numbers, E equals 1143 GPa and (upsilon) equals 0.0691, which are quite compatible with available experimental evidence. Our measurements of the biaxial modulus, E' equals E(1 - (upsilon) ), made use of the bulge test method to characterize the elastic behavior of both microwave-power and hot-filament assisted CVD diamond films. High- quality deposits yield E' is congruent to 1180 GPa and E' is congruent to 1220 GPa for randomly orientated and (110) textured deposits, respectively: these results confirm that state-of-the-art deposits exhibit elastic properties that are in accord with the measured stiffnesses of natural single- crystal diamond. The residual hydrogen content strongly impacts the elastic behavior and appears to be responsible for the degradation of the modulus observed in this and previous work.

^{-1}band-mode cutoff, which is induced by nitrogen-associated defect centers and yields the precise positions of sixteen zone-edge CP phonons. In conjunction with the triply-degenerate zone-center mode, this set of phonons then provides the basis for predicting the positions of second-order optical features through simple summations. Taking the selection rules into account, the procedure yields excellent results, not only in terms of CVD-diamond IR spectra, but also in regard to earlier measurements of the intrinsic two-phonon absorption coefficient of type-IIa natural diamond and the second-order polarization-dependent Raman-scatter characteristics recorded by Solin and Ramdas.

Monolithic diamond deposits lack the degree of transparency required for operation as transmissive optics elements in the mid-IR: at longer wavelengths (LWIR), it can be reasonably expected that singlephonon absorptions will be tolerable in the sense that self-emission phenomena at elevated temperatures should not be catastrophic. Besides surface hardness, the features that confer diamond its advantage are the high thermal conductivity and the low thermal expansion, which indicate that diamond has orders of magnitude more thermal shock resistance than some of the best competing materials. There is little doubt that the "new diamond" technology will provide a credible, if not outstanding LWIR dome material for tactical missiles operating at speeds up to but not beyond Mach 4 in the atmosphere.

Defect-free, single-crystal diamond also emerges as a promising candidate material for high-average-power laser window applications in the near-IR. The power-handling capability (<1 MW independently of the window size! will be limited by la) thermally induced optical distortion, which can only be eliminated if absorption-free anti-reflection coatings become available, and (b) the edge heat-transfer coefficient, which must be greatly enhanced to take advantage of the exceptional thermal conductivity of diamond at low temperatures. Pressure-induced and thermally-induced stresses are of no consequence, but peak laser intensities in excess of, say 1 GW/cm

^{2}should be avoided because of unfavorable non-linear refractive index characteristics.

**Proceedings Volume Editor**(2)

This will count as one of your downloads.

You will have access to both the presentation and article (if available).

View contact details

__sign in__to access your institution's subscriptions.

**To obtain this item,**you may purchase the complete book in print format on SPIE.org.