ZERODUR®

For several decades, the unique technical properties of ZERODUR® glass-ceramic have made it ideal for a vast range of applications that rely on exceptionally low-thermal-expansion materials. It's also now the industry standard for ultra-precise mirror substrates in astronomy.

Low-thermal-expansion glass-ceramic with exceptional properties

Extremely low-thermal-expansion

When ZERODUR® is exposed to heat, the micro-crystals of its two-phase microscopic system contract, while their surrounding glass matrix expands. This results in an overall near-zero expansion, achieved with an accuracy down to 0 ± 7 ppb/K at ambient temperature.

Strong performance under extreme conditions

As well as its inertness to large temperature differences, ZERODUR® is suitable for applications involving mechanical loads up to 100 MPa. We can help predict its lifetime under a variety of loads using our long-term expertise and data acquisition on breakage stress.

Homogeneous and reproducible

A major asset of ZERODUR® is its exceptional 3D homogeneity, not only in terms of low CTE, but also its remarkably low level of inclusions, striae and bulk stress. SCHOTT offers these properties up to dimensions of 4.25 m.

Customized shapes

ZERODUR® is available in a variety of highly customizable shapes. Advanced grinding and polishing results in a roughness below several nanometers, which provides the perfect substrate for high-tech coatings. Furthermore, it can be light-weighted by up to 80% while keeping its mechanical stability.

Thermal expansion

CTE tolerances of ZERODUR®

By default, the mean coefficient of thermal expansion (CTE) of ZERODUR® is measured within the temperature range of 0°C to 50°C. Five expansion classes are differentiated as follows:

CTE Grades CTE (0°C; 50°C)*
ZERODUR® Expansion Class 2 0 ± 0.100 ・ 10-6/K
ZERODUR® Expansion Class 1 0 ± 0.050 ・ 10-6/K
ZERODUR® Expansion Class 0 0 ± 0.020 ・ 10-6/K
ZERODUR® Expansion Class 0 SPECIAL 0 ± 0.010 ・ 10-6/K
ZERODUR® Expansion Class 0 EXTREME 0 ± 0.007 ・ 10-6/K
ZERODUR® TAILORED

TAILORED ± 0.020・10-6/K 
(± 0.010・10-6/K upon request) 
Optimized for application temperature

*CTE (0°C; 50°C) describes the linear mean coefficient of thermal expansion in the temperature 0°C to 50°C.

 

Maximum application temperature 600°C.

Upon request, ZERODUR® is available for customized temperature ranges.

We offer expansion class 0 or better optimized for your individual application.

 

CTE homogeneity

Homogeneity is evaluated by measuring CTE samples homogeneously distributed throughout the blank and calculating the difference in CTE between the highest and the lowest value measured.

The homogeneity of linear expansion can be guaranteed in the following weight classes:

CTE (0°C; 50°C) Homogeneity Tolerances

  • up to 18 tons: < 0.03 ・ 10-6/K
  • up to 6 tons: < 0.02 ・ 10-6/K
  • up to 0.3 tons: < 0.01 ・ 10-6/K

 

CTE distribution within a 1.5 m diameter blank with a measured CTE homogeneity of 0.004 · 10-6/K

4-SCHOTT-Zerodur_EN_563px.png

 

CTE tolerances of ZERODUR® K20

ZERODUR® K20, a high-temperature version of ZERODUR®, has been optimized to withstand higher application temperatures.

Mean coefficient of linear thermal expansion of ZERODUR® K20

  • CTE (20°C; 700°C): 2.4・10-6/K
  • CTE (20°C; 300°C): 2.2・10-6/K
  • CTE (0°C; 50°C): 1.6 ・ 10-6/K

Maximum application temperature 850°C.

Internal quality

If no quality is specified upon receipt of an order, then ZERODUR® will be supplied in standard quality. Individual specifications for internal quality can be fulfilled upon request.

 

Inclusions

Although the defect level is low, the main inclusions found in ZERODUR® are bubbles. During inspection of ZERODUR® parts, all inclusions with a diameter > 0.3 mm are taken into consideration. If an inclusion has a shape other than spherical, the average diameter is reported as the mean of the length and width. ZERODUR® is available in six different inclusion quality levels, which are defined according to the dimension of your part.

Quality levels for inclusions in ZERODUR®

Average number of inclusions per 100 cm3:

Standard 5.0
Class 4 5.0 
Class 3 4.0
Class 2 3.0
Class 1
2.0
Class 0
1.0

 

Maximum diameter of individual inclusions in mm for different diameters or diagonals of the ZERODUR® part:

In the critical volume < 500 mm  < 2000 mm < 4000 mm 
Standard 1.4 2.0  3.0 
Class 4 1.2  1.8  2.5 
Class 3 1.0 1.6  2.0 
Class 2 0.8 1.5  1.8 
Class 1 0.6 1.2  1.6 
Class 0 0.4 1.0  1.5 

 

In the uncritical volume
< 500 mm < 2000 mm < 4000 mm
Standard 3.0  6.0 10.0
Class 4 2.0 5.0  8.0 
Class 3 1.5 4.0  6.0 
Class 2 1.0 3.0  6.0 
Class 1 0.8 3.0  6.0 
Class 0 0.6 3.0  6.0 

Individual specifications upon request.

  

Bulk stress

The bulk stress birefringence of ZERODUR® is recorded in path difference per thickness in inspection direction. For discs it is measured in axial direction at 5 % of the diameter from the edge. For rectangular plates, the measurement is performed in the middle of the longer side perpendicular to the plate‘s surface.

Quality levels for bulk stress in ZERODUR®

Bulk stress birefringence [nm/cm] for parts with diameters or diagonals:


< 500 mm < 2000 mm  < 4000 mm
Standard 6         12        15       
Class 4 4 10 12
Individual specifications upon request

 

Striae

Additionally to the bulk stress birefringence, the stress birefringence induced by local striae is classified as a function of part diameter.

Stress birefringence caused by striae [nm/striae] for parts with diameters or diagonals:


< 500 mm < 2000 mm  < 4000 mm
Standard 60  60  60 
Class 4  45 45  45 
Class 3 30  30  30 
Class 2  30  30 
Class 1  30 

Processing

ZERODUR® is processed into complex geometries based on technical drawings and specifications from our customers. Our application and process engineers support you during the design phase of your product to get the most out of the ZERODUR® properties for your individual application. We also provide finite-element modelling and special quality requirements upon request.

5-axis CNC grinding machines allow for precise fabrication of ZERODUR® parts up to 4.25 m in diameter. The highlight of ZERODUR® processing is its light-weighting by grinding challenging aspect ratios of pocket heights to rib thickness used for parts with strict weight requirements.

By single-side and double-side polishing, we offer different surface-quality grades for dimensions up to 500 mm. Depending on the size of your part, a roughness down to the sub-nanometer range can be achieved.

As ZERODUR® acts as a very good substrate for coating, several coatings from standard aluminum to complex customized coatings are available for parts smaller than 300 mm. Our coating experts are ready to support you in choosing the coating that matches your specifications best.

 

Proposed CNC grinding tolerances for dimensions and shapes

Dimension < 2000 mm  Tolerances [mm] Thighter tolerances [mm]*
Length, width, height
± 0.3 ± 0.1
Diameter ± 0.3 ± 0.1
Angle ± 5’ ± 1’
Flatness ** 0.1 - 0.2 0.1
Cylindricity ** 0.1 0.1
Profile ** 0.2 0.1
Parallelism ** 0.1 - 0.2  0.1 
Position ** 0.1 0.1
Concentricity ** 0.1 0.1
Run-out ** 0.1 0.1
* tighter tolerances depend on the size and geometry. They cannot be combined freely.

** according ISO 1101

 

Dimension ≤ 4000 mm
Tolerances [mm]
Thighter tolerances [mm]*
Length, width, height ± 0.4
± 0.2
Diameter ± 0.4 ± 0.2 
Angle ± 5’ ± 1’
Flatness ** 0.2 0.1 
Cylindricity ** 0.2 0.1
Profile ** 0.4 0.2
Parallelism ** 0.2 0.1
Position ** 0.2 0.1
Concentricity ** 0.2 0.1
Run-out ** 0.2 0.1
* tighter tolerances depend on the size and geometry. They cannot be combined freely.

** according ISO 1101

Physical properties

Bending stress and lifetime calculation

ZERODUR® is the material of choice when it comes to excellent thermal properties and precision in high-tech applications. Often these applications also require to withstand certain mechanical loads, such as continuously as in telescope mirror holders or short-term during rocket launch.

The key factor to be evaluated to quantify the breakage stress of ZERODUR® is the surface quality, especially the occurrence of microcracks. In general, applying loads below 10 MPa tensile stress does not demand any special breakage analysis of ZERODUR®.

SCHOTT’s exhaustive data on the breakage events of ground ZERODUR® samples has shown that it can withstand long-term (tens of years) mechanical loads of 30 to 100 MPa. This is much higher than previously predicted. Using a three-parameter Weibull distribution, we are happy to discuss the ZERODUR® lifetime under your individual long-term mechanical loads.

 

Typical mechanical and optical properties

ZERODUR® ZERODUR® K20
Thermal conductivity λ at 20°C [W/(m・K)] 1.46 1.63
Thermal diffusivity index a at 20°C [10-6m2/s] 0.72 -
Heat capacity cp at 20°C [J/(g · K)] 0.80 0.90
Young's modulus E at 20°C [GPa]-mean value 90.3 84.7
Poisson‘s ratio 0.24 0.25
Density ρ [g/cm3] 2.53 2.53
Knoop Hardness HK 0,1/20 (ISO9385) 0.1 - 0.2 0.05
Refractive index nd 0.1 0.05
Abbe number νd 0.1 0.05
Internal transmittance Ti at 580 nm / 5 mm thickness 0.95 -
Internal transmittance Ti at 580 nm / 10 mm thickness 0.9 -
Stress optical coefficient K at λ = 589.3 nm [10-6MPa-1] 3 -
Electrical resistivity ρ at 20°C [Ω · cm] 2.6 · 1013 -
Tk100 [°C], Temperature for ρ = 108 [Ω · cm] 178 -

 

 

 

Chemical properties

At room temperature, most acids, alkalis, salts and dye solutions leave no residual traces on ZERODUR® surfaces. It can be etched by hydrofluoric acid as well as concentrated sulfuric acid at elevated temperatures. Furthermore, construction materials such as mica, chamotte, MgO and SiO2 do not react noticeably with ZERODUR® (up to 600°C for 5 h). By contrast, enamel reacts above 560°C by having its surface destroyed. 

Based on the good chemical resistance of the material, coatings such as mirrors are removable in a reproducible manner. The polished surface is simply cleaned and recoated by an optimized protocol.

 

Typical chemical properties

  ZERODUR® ZERODUR® K20
Hydrolytic resistance class (ISO 719) HGB 1  -
Acid resistance class (ISO 8424) 1.0
 -
Alkali resistance class (ISO 10629) 1.0  -
Climate resistance Class 1  -
Stain resistance Class 0  -
Helium permeability [Atoms/(cm · s · bar)] at 20°C 1.6 · 106  -
Helium permeability [Atoms/(cm · s · bar)] at 100°C 5.0 · 107  -
Helium permeability [Atoms/(cm · s · bar)] at 200°C 7.2 · 108  -

Selected Publications

No.         Year Title Authors Publications
[1-14]         2018 Advices for the use of ZERODUR® at higher temperatures R. Jedamzik, T. Westerhoff Proc. SPIE Vol. 10706
[1-13] 2017 Homogeneity of the coefficient of linear thermal expansion of ZERODUR: a review of a decade of evaluations R. Jedamzik, T. Westerhoff Proc. SPIE Vol. 10401
[1-12] 2016  ZERODUR® thermo-mechanical modelling and advanced dilatometry for the ELT generation R. Jedamzik, C. Kunisch, T. Westerhoff Proc. SPIE Vol. 9912
[1-11] 2016 Effects of thermal inhomogeneity on 4m class mirror substrates R. Jedamzik, C. Kunisch, T. Westerhoff Proc. SPIE Vol. 9912
[1-10] 2016 Progress on glass ceramic ZERODUR® enabling nanometer precision Ralf Jedamzik, Clemens Kunisch, Johannes Nieder, Peter Weber, Thomas Westerhoff Proc. SPIE Vol. 9780
[1-10] 2016 ZERODUR® thermo-mechanical modelling and advanced dilatometry for the ELT generation Ralf Jedamzik, Clemens Kunisch, Thomas Westerhoff Proc. SPIE Vol. 9912
[1-10] 2016 Next generation dilatometer for highest accuracy thermal expansion measurement of ZERODUR® R. Jedamzik, A. Engel, C. Kunisch, G. Westenberger, P. Fischer, T. Westerhoff Proc. SPIE Vol. 9574
[1-8] 2014 ZERODUR® TAILORED for cryogenic application R. Jedamzik, T. Westerhoff Proc. SPIE. Vol. 9151
[1-7] 2013 ZERODUR®: progress in CTE characterization R. Jedamzik, C. Kunisch, T. Westerhoff Proc. SPIE Vol. 8860
[1-6] 2013 Zero expansion glass ceramic ZERODUR® roadmap for advanced lithography T. Westerhoff, R. Jedamzik, P. Hartmann Proc. SPIE Vol. 8683
[1-5] 2010 Modelling of the thermal expansion behavior of ZERODUR® at arbitrary temperature profiles R. Jedamzik, T. Johansson, T. Westerhoff Proc. SPIE Vol. 7739
[1-4] 2009 CTE characterisation of ZERODUR® for the ELT century R. Jedamzik, T. Döhring, T. Johansson, P. Hartmann, T. Westerhoff Proc. SPIE Vol. 7425
[1-3] 2006 Homogeneity of the linear thermal expansion coefficient of ZERODUR® measured with improved accuracy  R. Jedamzik, R. Müller, P. Hartmann  Proc. SPIE Vol. 6273
[1-2] 2006 Influence of striae on the homogeneity of the linear thermal expansion coefficient of ZERODUR®  R. Jedamzik, P. Hartmann Proc. SPIE Vol. 6288
[1-1] 2005 Homogeneity of the coefficient of linear thermal expansion of ZEDRODUR®  R. Jedamzik, T. Doehring, R. Mueller, P. Hartmann  Proc. SPIE Vol. 5868
No.         Year Title Authors Publications
[3-20]              
 2019  ZERODUR® as a dimensionally stable mirror substrate material for spaceborne telescopes  Tony Hull, Antoine Carre, Ralf Jedamzik  Proc. SPIE Vol. 11180 (open access)
 [3-19]  2018  Advances in ZERODUR® manufacturing for space and ground based telescopes  T. Westerhoff, T. Werner  Proc. SPIE Vol. 10706
 [3-18]  2017  ZERODUR® expanding capabilities and capacity for future spaceborne and ground-based telescopes  T. Westerhoff, T. Werner  Proc. SPIE Vol. 10401
 [3-17]  2016  Production of ELZM mirrors: performance coupled with attractive schedule, cost, and risk factors  A. Leys, T. Hull, T. Westerhoff  Proc. SPIE Vol. 9911
 [3-16]  2016  Use of updated material properties in parametric optimization of spaceborne mirrors  T. Hull, T. Westerhoff, G. Weidmann, R. Kirchhoff  Proc. SPIE Vol. 9904
 [3-15]  2015  Cost-optimized methods extending the solution space of lightweight spaceborne monolithic ZERODUR® mirrors to larger sizes  A. Leys, T. B. Hull, T. Westerhoff  Proc. SPIE Vol. 9573
 [3-14]  2015  Selection considerations between ZERODUR® and silicon carbide for dimensionally-stable spaceborne optical telescopes in low-earth-orbit  T. Hull, A. Leys, T. Westerhoff  Proc. SPIE Vol. 9573
 [3-13]  2014  Lightweight ZERODUR® mirror blanks: recent advances supporting faster, cheaper, and better spaceborne optical telescope assemblies  T. Hull, T. Westerhoff  Proc. SPIE. Vol. 9241
 [3-12]  2014  Extreme lightweight ZERODUR® mirrors (ELZM): supporting characteristics for spaceborne applications  T. Hull, T. Westerhoff  Proc. SPIE. Vol. 9143
 [3-11]  2014  ZERODUR® iso-grid design of a 3 m class light weighted mirror blank for the E-ELT M5  R. Jedamzik, A. Leys, V. Seibert, T. Westerhoff  Proc. SPIE. Vol. 9151
 [2-2] 2007   Strength aspects for the design of ZERODUR® glass ceramics structures  P. Hartmann, K. Nattermann, T. Doehring, M. Kuhr, P. Thomas, G. Kling, P. Gath, S. Lucarelli  Proc. SPIE Vol. 6666
 [3-9]  2014  Lightweight ZERODUR®: a cost-effective thermally stable approach to both large and small spaceborne telescopes  T. Hull, T. Westerhoff  Proc. SPIE. Vol. 9070
 [3-8]  2013  Practical aspects of specification of extreme lightweight ZERODUR® mirrors for spaceborne missions  T. Hull, T. Westerhoff, A. Lays, J. Pepi  Proc. SPIE Vol. 8836
 [3-7]  2012  Game-changing approaches to affordable advanced lightweight mirrors II: new cases analyzed for extreme ZERODUR® lightweighting and relief from the classical polishing parameter constraint  T. Hull, T. Westerhoff, J. W. Pepi, R. Jedamzik, G. J. Gardopee, F. Piché, A. R. Clarkson, A. Leys, M. Schaefer, V. Seibert  Proc. SPIE Vol. 8450
 [3-6]  2011  Game-changing approaches to affordable advanced lightweight mirrors: Extreme ZERODUR® lightweighting and relief from the classical polishing parameter constraint  T. Hull, T. Westerhoff et al.  Proc. SPIE Vol. 8125
 [3-5]  2011  Design and fabrication of a 3m class light weighted mirror blank for the E-ELT M5  R. Jedamzik, V. Seibert, A. Thomas, T. Westerhoff, M. Müller, M. Cayrel  Proc. SPIE Vol. 8126
[3-4]   2010  Lightweight high-performance 1-4 meter class spaceborne mirrors: emerging technology for demanding spaceborne requirements  T. Hull, P. Hartmann, A. R. Clarkson, J. M. Barentine, R. Jedamzik, T. Westerhoff  Proc. SPIE Vol. 7739
 [3-3]  2010  Manufacturing of the ZERODUR® 1.5 m primary mirror for the solar telescope GREGOR as preparation of light weighting of blanks up to 4 m diameter  T. Westerhoff, M. Schäfer, A. Thomas, M. Weisenburger, T. Werner, A. Werz  Proc. SPIE Vol. 7739
 [3-2]  2009  Heritage of ZERODUR® glass ceramic for space applications  T. Döhring, P. Hartmann, F.-T. Lentes, R. Jedamzik, M. J. Davis  Proc. SPIE Vol. 7425
 [3-1]  2007  Manufacturing of light weighted ZERODUR® components at SCHOTT  T. Döhring, A. Thomas, R. Jedamzik, H. Kohlmann, P. Hartmann  Proc. SPIE Vol. 6666
No.         Year Title Authors Publications
[2-13]    2019  Minimum lifetime of ZERODUR® structures based on the breakage stress threshold model: a review  Peter Hartmann  Optical Engineering Vol. 58, Issue 2 (open access)
 [2-12]  2018  The relation of surface treatment and sub-surface damage on ZERODUR®  R. Jedamzik, P. Hartmann, I. Burger, T. Westerhoff  Proc. SPIE Vol. 10706
 [2-11]  2017  ZERODUR®-bending strength: review of achievements  P. Hartmann  Proc. SPIE Vol. 10371
 [2-10]  2016  ZERODUR® strength modeling with Weibull statistical distributions  P. Hartmann  Proc. SPIE Vol. 9912 (open access)
 [2-9]            2015  ZERODUR®: new stress corrosion data improve strength fatigue prediction  P. Hartmann, G. Kleer  Proc. SPIE Vol. 9573
 
[2-8]
 2014  ZERODUR®: bending strength data for etched surfaces  P. Hartmann, A. Leys, A. Carré, F. Kerz, T. Westerhoff  Proc. SPIE. Vol. 9151
 [2-7]  2012  ZERODUR®, Deterministic approach for strength design  P. Hartmann  Optical Engineering 51(12)
 
[2-6]
 2012  ZERODUR® for stressed mirror polishing II: improved modeling of the material behavior  R. Jedamzik, C. Kunisch, T. Westerhoff, U. Müller, J. Daniel  Proc. SPIE Vol. 8450
 [2-5]  2011  ZERODUR®: new results on bending strength and stress corrosion  P. Hartmann  Proc. SPIE Vol. 8146
 [2-4]  2011  ZERODUR® for stress mirror polishing  R. Jedamzik, C. Kunisch, T. Westerhoff  Proc. SPIE Vol. 8126
 [2-3]  2009  ZERODUR® glass ceramics for high stress applications

 P. Hartmann, K. Nattermann, T. Döhring, R. Jedamzik, M. Kuhr, P. Thomas, G. Kling, S. Lucarelli

 Proc. SPIE Vol. 7425
 [2-2]  2007  Strength aspects for the design of ZERODUR® glass ceramics structures  P. Hartmann, K. Nattermann, T. Doehring, M. Kuhr, P. Thomas, G. Kling, P. Gath, S. Lucarelli  Proc. SPIE Vol. 6666
 [2-1]  2008  ZERODUR® glass ceramics: design of structures with high mechanical stresses  K. Nattermann, P. Hartmann, G. Kling, P. Gath, S. Lucarelli, B. Messerschmidt  Proc. SPIE Vol. 7018
No.         Year Title Author Publications
[4-18]       2020  ZERODUR® manufacturing capacity: ELT and more  T. Westerhoff, T. Hull, R. Jedamzik  Proc. SPIE Vol. 11116
 [4-17]  2020  Establishing a substrate manufacturing center for ZERODUR 4-meter diameter lightweight mirrors  T. Westerhoff, T. Hull, R. Jedamzik  Proc. SPIE Vol. 11117
 [4-16]  2020  Optimizing ZERODUR® mirror substrate fabrication processes for efficient optical fabrication  T, Hull, T. Westerhoff, R. Jedamzik  Proc. SPIE Vol. 11116
 [4-15]  2017  ZERODUR® 4-m blank surviving up to 20 g acceleration  T. Westerhoff, T. Werner, T. Gehindy  Proc. SPIE Vol. 10401
 [4-14]  2012  Performance of industrial scale production of ZERODUR® mirrors with diameter of 1.5 m proves readiness for the ELT M1 segments  T. Westerhoff, P. Hartmann, R. Jedamzik, A. Werz  Proc. SPIE Vol. 8444
 [4-13]  2012  Zero-expansion glass ceramic ZERODUR®: recent developments reveal high potential  P. Hartmann, R. Jedamzik, T. Westerhoff  Proc. SPIE Vol. 8450
 [4-12]  2011  Progress on 4 m class ZERODUR® mirror production  T. Westerhoff, S. Gruen, R. Jedamzik, C. Klein, T. Werner, A. Werz  Proc. SPIE Vol. 8126
 [4-11]  2010  ZERODUR® 8 m mirror for space telescope  P. Hartmann, T. Westerhoff, R. Reiter, R. Jedamzik, V. Wittmer, H. Kohlmann  Proc. SPIE Vol. 7731
 [4-10]  2009  Four decades of ZERODUR® mirror substrates for astronomy  T. Döhring, R. Jedamzik, T. Westerhoff, P. Hartmann  Proc. SPIE Vol. 7281
 [4-9]  2007  Mirrors for solar telescopes made from ZERODUR® glass ceramic  T. Döhring, R. Jedamzik, P. Hartmann  Proc. SPIE Vol. 6689
 [4-8]  2006  Properties of ZERODUR® mirror blanks for extremely large telescopes  T. Döhring, P. Hartmann, R. Jedamzik, A. Thomas, F.-T. Lentes  Proc. SPIE Vol. 6148
 [4-7]  2005  Status of ZERODUR® mirror blank production at SCHOTT  T. Doehring, P. Hartmann, R. Jedamzik, A. Thomas  Proc. SPIE Vol. 5869
 [4-6]  2004  ZERODUR® mirror blanks for ELTs: technology and production capacity at SCHOTT  T. Dohring, P. Hartmann, R. Jedamzik, A. Thomas  Proc. SPIE Vol. 5382
 [4-5]  2004  Production of the 4.1-m ZERODUR® mirror blank for the VISTA Telescope  T. Doehring, R. Jedamzik, V. Wittmer, A. Thomas  Proc. SPIE Vol. 5494
 [4-4]  2004  Forming mandrels for x-ray telescopes made of modified ZERODUR®  T. Doehring, R. Jedamzik, P. Hartmann, H. Esemann, C. Kunisch  Proc. SPIE Vol. 5168
 [4-3]  2004  100 years of mirror blanks from SCHOTT  P. Hartmann, H. F. Morian  Proc. SPIE Vol. 5382
 [4-2]  2003  ZERODUR® mandrels for the next generation of x-ray telescopes  T. Doehring, R. Jedamzik, A. Thomas, H. F. Morian  Proc. SPIE Vol. 4851
 [4-1]  2003  ZERODUR® for large segmented telescopes  H. F. Morian, P. Hartmann, R. Jedamzik, H. W. Hoeness  Proc. SPIE Vol. 4837

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