US20130251614A1

US20130251614A1 - Annealing of single crystals

Info

Publication number: US20130251614A1
Application number: US13/899,708
Authority: US
Inventors: Dominique Richaud; Alain Iltis; Vladimir Ouspenski
Original assignee: Individual
Current assignee: Individual
Priority date: 2008-03-31
Filing date: 2013-05-22
Publication date: 2013-09-26
Also published as: US8470089B2; FR2929296B1; US20090246495A1; FR2929296A1

Abstract

The invention relates to a process for manufacturing a single crystal comprising a rare-earth halide, having improved machining or cleavage behaviour, comprising heat treatment in a furnace, the atmosphere of which is brought, for at least 1 hour, to between 0.70 times T_mand 0.995 times T_mof a single crystal comprising a rare-earth halide, T_mrepresenting the melting point of said single crystal, the temperature gradient at any point in the atmosphere of the furnace being less than 15 K/cm for said heat treatment. After carrying out the treatment according to the invention, the single crystals may be machined or cleaved without uncontrolled fracture. The single crystals may be used in a medical imaging device, especially a positron emission tomography system or a gamma camera or a CT scanner, for crude oil exploration, for detection and identification of fissile or radioactive materials, for nuclear and high-energy physics, for astrophysics or for industrial control.

Description

The invention relates to a heat treatment applied to single crystals of rare-earth halides to improve their mechanical properties, and also to the use of these single crystals treated by the process to produce large-size parts for manufacturing detectors of ionizing radiation and large cleaved parts. The compositions of the single crystals in question in the invention are scintillator materials based on rare-earth halides.
The single crystals in question in the present invention are those directly obtained by crystal growth or those obtained by fracture, generally uncontrolled, of larger single crystals, for example obtained by crystal growth. Scintillator detectors are widely used for detecting gamma rays, X-rays, high-energy cosmic rays, charged particles having an energy between 1 keV and 10 MeV, between 1 keV and 1 Gev, between 1 keV and 10 GeV, thermal neutrons (the energy of which is typically less than 0.1 eV).
Scintillator detectors are used in numerous applications. Mention may be made, as non-exhaustive examples, of medical imaging (especially positron emission tomography systems, gamma cameras, CT scanners), crude oil exploration (well-logging), equipment for detecting and identifying fissile or radioactive materials, experiments in nuclear and high-energy physics, detectors for astrophysics or else industrial control.
A scintillator detector is composed of a scintillator material which converts the energy of the particles or radiation absorbed to ultraviolet or visible or infrared light and a photon collector which captures the light emitted and converts it to an electrical signal. The scintillator materials are in the form of a powder, of single crystals, of transparent polycrystalline ceramics, of glasses, of plastics and of liquids. The single-crystal materials, that is to say parts which, on the scale of use, are composed of a single crystal (at most a few crystals), are particularly suitable for producing scintillators. The use of single crystals has several advantages. Compared to polycrystalline materials, for parts of large thickness, the single crystals offer a better transparency and therefore a better extraction of the light due to the absence of grain boundaries and defects responsible for the dissipation of light in the solid. In the applications, when it is possible, the single crystals are preferred materials for scintillation. The photon collectors may be photomultiplier tubes or any light converter compatible with the emission wavelength of the material (example: photodiodes, avalanche photodiodes, etc.).
Rare-earth halides are materials known in the field of scintillator materials. The article by K. Krämer et al. (Development and characterization of highly efficient new cerium doped rare earth halide scintillator materials, J. Mater. Chem., 2006, 16, pp. 2773-2780), gives several examples of these scintillator crystals doped with cerium and which are characterized by a combination of good scintillation properties such as good energy resolution, a high light yield and a rapid response. For example, in this publication, LaBr₃doped with 5 mol % of cerium has an energy resolution of 2.6% under excitation at 662 keV (main gamma emission of ¹³⁷Cs), a light yield of 70 000 photons per MeV and a scintillation decay time of 16 ns. Another example cited is cerium-doped Lul₃which has an energy resolution of 3.3% at 662 keV, a light yield of 95 000 photons per MeV and a scintillation decay time of 24 ns for the main light component. Also, the publication by C. van Eijk et al. (Development of elpasolite and monoclinic thermal neutron scintillators, 2005 IEEE Nucl. Sci. Symp. Conf. Record, 1, pp. 239-243) has the properties of compounds based on rare-earth halides for the simultaneous detection of neutrons and gamma rays. For example, Rb₂LiYBr₆doped with 0.5 mol % of Ce has a light yield of 18 000 photons per MeV at 662 keV and a light yield of 65 000 photons per neutron (thermal neutrons). Other examples taken from the same article are Cs₂LiYCl₆doped with 0.1 mol % of cerium, Cs₂LiLaCl₆doped with 1 mol % of cerium, Rb₂LiYl₆doped with 0.5 mol % of cerium, and Li₃YBr₆doped with 0.5 mol % of cerium which respectively have light yields at 662 keV of 18 000 photons per MeV, 28 000 photons per MeV, 7000 photons per MeV and 6000 photons per MeV. Other non-exhaustive examples of compounds based on rare-earth halides for scintillation cited in the literature are: LaBr₃doped with praseodymium (J. Glodo et al., IEEE Nucl. Sci. Symp. Conf. Record, 2005, pp. 98-101), GdBr₃doped with cerium (E. V. D. van Loef et al., Optics Communications, 189, 2001, pp. 297-304), LuCl₃and LuBr₃doped with cerium (O. Guillot-Noël et al., J. Luminescence, 85, 1999, pp. 21-35), RbGd₂Br₇doped with cerium (W. Moses et al., Nucl. Instruments and Methods in Physics Research, A, 537, 2005, pp. 317-320), Cs₂LiYCl₆doped with praseodymium (E. V. D. van Loef et al., IEEE Trans. Nucl. Sci., 52, 5, 2005, pp. 1819-1822), K₂LaBr₅doped with cerium (U. N. Roy et al., “Hard X-Ray and Gamma-Ray Detector Physics VII”, Proceedings of the SPIE, 5922, 2005, pp. 30-34).
Rare-earth halides are difficult to produce in the form of single crystals. This is because these compounds are very reactive with oxygen and water vapour. The chemical reaction at high temperature with oxygen and water vapour is irreversible and the crystals must therefore be crystallized in such a way that any reaction with these elements is impossible. The solution is to carry out the crystal growth in a device that is airtight, under vacuum or under an atmosphere that is not reactive with respect to the crystal. Another aspect is the crystal growth, without fracturing and without residual mechanical stresses, of single crystals that are sufficiently large to produce large-size detectors. This is because mechanical stresses of thermal origin are created within the crystals during growth and during cooling in the growth furnace (J. Völkl, “Stress in cooling crystal” in Handbook of Crystal Growth, Ed. North Holland, Edited by D. T. J. Hurle, 1994, ISBN 0-444-81554-6, pp. 821-874).
The mechanical stresses may be very high and may even exceed the strength of the materials and cause fracturing of the single crystals into several pieces. Even when the process is optimized to avoid fracturing during crystal growth and cooling, a large portion of residual stresses remain in the single crystals. In the best of cases, these residual stresses are not sufficient to cause fracturing of the crystals but, during the machining steps (for example cutting, milling, turning, polishing, etc.) microcracks develop in the materials and propagate under the effect of the residual stresses, which finally causes fracturing of the single crystals. This problem makes it very difficult to produce single-crystal parts for the production of detectors, especially to produce large-size single-crystal parts. The effect of the residual stresses in also important in the case of producing parts by the cleavage method. Cleavage is a distinctive feature that certain single crystals have of fracturing along certain precise crystalline planes when they are subjected to an impact or to a mechanical stress. The cleaved surfaces are extremely flat, even and have no roughness and they may be used for producing very high quality surfaces. In the single crystals that contain residual stresses, the cleavage process is normally disrupted by the formation of numerous macroscopic steps and/or parasitic breaks that do not follow the crystalline cleavage plane. The cleaved surface will then be highly irregular. A good cleaved surface has few or no macroscopic steps and the heights of the steps remain low. A person skilled in the art easily distinguishes a cleaved surface from a surface obtained by crystal growth or by mechanical cutting.
In the case of single crystals based on rare-earth halides, the question of fracturing is extremely important as these materials have the characteristic of being very brittle. An illustration of the brittleness of these compounds is given in the article by K. Findley et al. (“Fracture and deformation behaviour of common and novel scintillating single crystals”, Proceedings of SPIE, The International Society for Optical Engineering, 2007, vol 6707, pp. 6707 06) which shows that the cerium-doped LaBr₃crystals have a very low fracture toughness. Obtaining large-size parts and parts with large cleaved surfaces is therefore a problem that is particularly difficult to solve for this type of single crystals.
The invention described here is a heat treatment which enables the elimination or the reduction of the residual stresses in single crystals after the crystal growth process has been carried out. The heat treatment of the invention is carried out by heating up to the treatment temperature, by maintaining this treatment temperature, then by cooling to ambient temperature. The treatment temperature is slightly below the melting point of the material treated. The gaseous atmosphere during the treatment is protective and makes it possible to prevent the reaction of the treated crystals with oxygen or water vapour.
The process according to the invention does not modify the scintillation performance of the annealed single crystals as can be the case in certain processes which are especially applied to the crystals of oxides. For example, as is described in U.S. Pat. No. 7,151,261, the temperature treatment of single crystals of lutetium orthosilicates under reactive atmospheres containing oxygen makes it possible to substantially improve the performances of the materials treated. The treatment is, in this case, carried out at temperatures much lower than the melting point of the treated crystals and the oxygen contained in the treatment atmosphere reacts with the treated materials.
The invention described here firstly relates to a process for manufacturing a single crystal comprising a rare-earth halide, having improved machining or cleavage behaviour, said process comprising heat treatment in a furnace, the atmosphere of which is brought, for at least 1 hour, to between 0.70 times T_mand 0.995 times T_mof a single crystal comprising a rare-earth halide, T_mrepresenting the melting point of said single crystal, the temperature gradient at any point in the atmosphere of the furnace being less than 15 K/cm and preferably less than 5 K/cm and more preferably less than 0.5 K/cm during said heat treatment.
It appears that this treatment enables the relaxation of the residual stresses via plastic rearrangements. After this step, well-controlled cooling makes it possible to avoid formation of new residual stresses in the single crystals. The invention can be applied to large-size single crystals, especially having a volume greater than 50 cm³, and even greater than 100 cm³, and even greater than 300 cm³, and even greater than 1850 cm³. After carrying out the treatment according to the invention, these single crystals may be machined or cleaved without uncontrolled fracture. The treatment according to the invention makes it possible, via machining or via the cleavage method, to produce large machined or cleaved surfaces with, for example, machined or cleaved surfaces greater than or equal to 5 cm², or even greater than or equal to 9 cm², or even greater than 12 cm², and also, via other methods, to manufacture very large parts with, for example, volumes greater than or equal to 50 cm³or even greater than or equal to 1850 cm³, on condition that the initial volumes and the initial sizes of the single crystals allow it.
The invention relates to a method of heat treatment for eliminating or reducing the residual stresses in single crystals comprising a rare-earth halide. In particular, the composition of the single crystal may correspond to the formula A_nLn_pX_(3p+n)in which Ln represents one or more rare-earth elements, that is to say an element chosen from Y, Sc and the lanthanide series from La to Lu, X represents one or more halogen atoms chosen from Cl, Br and I, and A represents one or more alkali metals such as Li, Na, K, Rb or Cs, n and p are numbers such that n is greater than or equal to zero and less than or equal to 3 and p is greater than or equal to 1.
In particular, the composition may have the formula A_nLn_(p−x)Ln′_xX_(3p+n)in which Ln represents one or more rare-earth elements, that is to say an element taken from Y, Sc and the lanthanide series from La to Lu and more particularly from Y, La, Gd, Lu or a mixture of these elements, Ln′ is a doping element, that is to say a rare-earth element and more particularly an element chosen from Ce, Pr and Eu, x is a number greater than or equal to 0.0005 and less than p. Examples of such crystals are:

- LaCl₃, which may especially be doped with 0.1 to 50 mol % of Ce (i.e. p=1 and x=0.001 to 0.5 in the formula);
- LnBr₃, which may especially be doped with 0.1 to 50 mol % of Ce (i.e. p=1 and x=0.001 to 0.5 in the formula);
- LaBr₃, which may especially be doped with 0.1 to 50 mol % of Ce (i.e. p=1 and x=0.001 to 0.5 in the formula);
- GdBr₃, which may especially be doped with 0.1 to 50 mol % of Ce (i.e. p=1 and x=0.001 to 0.5 in the formula);
- La_zLn_(1−z)X₃, which may especially be doped with 0.1 to 50 mol % of Ce (i.e. p=1 and x=0.001 to 0.5 in the formula), z possibly varying from 0 to 1, Ln being a rare earth other than La, X being a halogen such as mentioned previously;
- La_zGd_(1−z)Br₃, which may especially be doped with 0.1 to 50 mol % of Ce (i.e. p=1 and x=0.001 to 0.5 in the formula), z possibly varying from 0 to 1;
- La_zLu_(1−z)Br₃, which may especially be doped with 0.1 to 50 mol % of Ce (i.e. p=1 and x=0.001 to 0.5 in the formula), z possibly varying from 0 to 1;
- Ln_zLn″_(1−z)X_3(1−y)X′_3yin which Ln and Ln″ are two different rare earths, X and X′ being two different halogens, in particular CI, Br or I, z possibly varying from 0 to 1, and y possibly varying from 0 to 1;
- RbGd₂Br₇, which may especially be doped with 0.1 to 50 mol % of Ce (i.e. n=1, p=2 and x=0.002 to 1 in the formula);
- RbLn₂Cl₇, which may especially be doped with 0.1 to 50 mol % of Ce (i.e. n=1, p=2 and x=0.002 to 1 in the formula);
- RbLn₂Br₇, which may especially be doped with 0.1 to 50 mol % of Ce (i.e. n=1, p=2 and x=0.002 to 1 in the formula);
- CsLn₂Cl₇, which may especially be doped with 0.1 to 50 mol % of Ce (i.e. n=1, p=2 and x=0.002 to 1 in the formula);
- CsLn₂Br₇, which may especially be doped with 0.1 to 50 mol % of Ce (i.e. n=1, p=2 and x=0.002 to 1 in the formula); - K₂LaCl₅, which may especially be doped with 0.1 to 50 mol % of Ce (i.e.

n=2, p=1 and x=0.001 to 0.5 in the formula);

- K₂Lal₅, which may especially be doped with 0.1 to 50 mol % of Ce (i.e. n=2, p=1 and x=0.001 to 0.5 in the formula) and
- Cs_(2−z)Rb_zLiLnX₆, where X is either Cl or Br or I, Ln is Y or Gd or Lu or Sc or La, where z is greater than or equal to 0 and less than or equal to 2.

Crystals which may be doped with different molar percentages of Ce (i.e. n=3, p=1 and 0.0005≦x<1 in the formula).
The use of the treatment process according to the invention makes it possible to prevent fracturing of large brittle single crystals during all the steps in the production line. This treatment also facilitates the production of parts via the cleavage method.
As is presented in WO 3106741, it is preferable to use graphite crucibles for handling rare-earth halides. For the heat treatment according to the invention, the single crystals are placed in high-purity graphite crucibles closed by high-purity graphite lids.
The heat treatment according to the invention is carried out in a furnace which has a high thermal homogeneity, so as to effectively reduce the stresses in the single crystals. This is because the presence of high thermal gradients in the furnace during the treatment would lead to the formation of new stresses which could cause fracturing of the crystal. In the furnace, the local temperature gradient is, at any point, less than 15 K/cm, preferably less than 5 K/cm and more preferably less than 0.5 K/cm. This homogeneity in the furnace atmosphere around the part to be treated has the objective of a high temperature homogeneity of the part itself. The part treated is therefore also homogeneous during the period it is held at temperature.
It is recalled that in the crystal growth processes for single crystals based on a rare-earth halide, the environment of the crystal has high temperature gradients, well above 15 K/cm.
The heat treatment according to the invention is carried out in an airtight furnace. The compounds based on rare-earth halides are very reactive at high temperature with oxygen and water vapour and the heat treatment must be carried out under a controlled atmosphere. The atmosphere may be dynamic (continuous pumping under vacuum or gas purging throughout all the steps of the heat treatment) or else static (filling the furnace with gas or putting it under a vacuum at the start of the heat treatment). The atmosphere for the treatment is vacuum or inert gases (with a low residual content of oxygen and of water vapour) such as, for example, nitrogen (N₂), helium (He), argon (Ar), or halogen gases such as, for example, chlorine (Cl₂), bromine (Br₂), iodine (I₂), hydrogen chloride (HCl), hydrogen bromide (HBr), hydrogen iodide (HI); hydrogen (H₂); or any mixture of these gases. Nitrogen and argon atmospheres are particularly suitable as these gases can be handled easily.
At temperatures close to the melting point of the material, the residual elastic stresses may be relaxed via plastic rearrangements. The heat treatment temperature is chosen as a function of the melting point (denoted T_m) of the material treated and is expressed in kelvin (T_m[K]=273+T_m[° C.]). The pertinent treatment temperatures are between 0.70 times T_mand 0.995 times T_m. The temperature range between 0.9 times and 0.995 times T_mis preferred. The duration of the temperature hold must be long enough to allow thermal homogenization within the single crystals and also elimination of the residual stresses by plastic deformation as the accomplishment of the two mechanisms is highly dependent on time (kinetic aspect of the phenomena involved). At the same time, the sizes of the single crystals have a great influence on the treatment time necessary to successfully carry out these two mechanisms: the larger the sizes are, the longer the temperature hold time will be. It is advisable that the treatment temperature be maintained between 1 to 120 hours, depending on the sizes of the single crystals to be treated. Hold times between 15 hours and 24 hours are particularly suitable.
Because the heat transfer coefficients of the materials control the transfer of heat in the single crystals, the heating and cooling rates must be well controlled in order to avoid the formation of temperature gradients (between the edges and the centre) and therefore the formation of mechanical stresses of thermal origin. This aspect is particularly important for the cooling as too rapid a cooling will lead to the formation of new stresses and will destroy the positive effect of the heat treatment. Very slow cooling rates may be used, however the heat treatment duration will then be very long which will considerably increase the cost of the treatment process. The rates are chosen so as to optimize both the efficiency (elimination or reduction of the stresses) and the duration of the annealing cycle. For the heat treatment according to the invention, the heating and cooling rates of the atmosphere in the furnace are chosen between 1 K/h and 30 K/h. Rates between 1 K/h and 10 K/h are particularly suitable. Thus, in the process according to the invention, before the heat treatment of at least one hour, the temperature of the furnace is raised to the temperature of the heat treatment with a rate between 1 K/h and 30 K/h. For the cooling which follows the heat treatment of at least one hour, the temperature decrease rate between the temperature of the heat treatment and 100° C. is between 1 K/h and 30 K/h. The temperature decrease rate between 100° C. and ambient temperature is less critical, but it is nevertheless recommended to continue to cool slowly. Respecting these temperature rises and decreases makes it possible to limit the risks of fracture.
The conditions which have just been given for the heat treatment must be applied simultaneously throughout the whole environment of the part to be treated in order to induce a high temperature homogeneity for the whole of the part to be treated (the whole crystal or one of its blocks obtained by fracturing), and not only over one of its parts.
The invention results in large-size single crystals that are cleaved without unwanted cracking or breaking. In particular, perfect cleavage along the crystallographic planes (10 10) may be carried out on a single crystal of hexagonal crystal structure having a P6₃/m space group, which includes, in particular, LaCl₃, CeCl₃, NdCl₃, PrCl₃, SmCl₃, EuCl₃, GdCl₃, LaBr₃, CeBr₃, PrBr₃, and also the mixtures of at least two of these halides (especially LaCl₃and LaBr₃, this mixture possibly being doped by a dopant such as Ce or Pr), these halides possibly being doped by a dopant such as Ce or Pr, and this being for a large single crystal (volume greater than 50 cm³and even greater than 1850 cm³).
The invention also allows the machining of large single crystals or of blocks of single crystals without unwanted cracking or breaking. The machining operations comprise, for example, cutting, milling, turning and polishing. The heat treatment according to the invention may advantageously be carried out in the absence of oxygen and water, depending on the degree of sensitivity to oxidation of the crystal, such as, for example, under vacuum, or in an inert atmosphere such as under nitrogen or under argon. In particular, for a given rare earth, the iodide is more sensitive than the bromide which is itself more sensitive than the chloride. The importance of the precautions to be taken from this point of view therefore follow this order.

EXAMPLE 1

Heat treatment of an LaBr₃Single Crystal Doped with 5 mol % of Cerium

The melting point of LaBr₃is 788° C. (1061 K). A non-fractured single crystal of LaBr₃:Ce was produced and cooled to ambient temperature. The crystal was placed in a high-purity graphite crucible. The crucible was closed by a high-purity graphite lid. The crucible containing the crystal was then introduced into the heat treatment furnace. The furnace was hermetically sealed and an inert atmosphere was set up inside the latter by means of a continuous purge of high-purity nitrogen (flow rate of 20 L/min). The heat treatment consisted of a heating ramp of 10 K/h followed by a temperature hold at 710° C. (983 K) (0.93 times the melting point T_mof LaBr₃) for 24 hours, then by a cooling ramp of 10 K/h down to ambient temperature. After the treatment, the single crystal was removed from the crucible and no fracture was visible. The single crystal was then machined to produce a 2″×2″ part (cylinder having a diameter of 2″ and a height of 2″, remember that 1″=2.54 cm) and a 3″33 3″ part for producing scintillator detectors. During the machining, no cracking was observed: the residual stresses had been removed during the heat treatment.

EXAMPLE 2

Heat Treatment of a Piece Derived from a Fractured Single Crystal of LaBr₃Doped with 5 mol % of Cerium

At the end of the crystal growth process, the single crystal was fractured into several pieces. One of these single-crystal pieces was sufficiently large (volume greater than 50 cm³) to allow the production of large-size detectors. In order to prevent fracturing while machining, the piece was treated by the process according to the invention. The piece was loaded into a high-purity graphite crucible closed by a high-purity graphite lid. The crucible containing the crystal was loaded into a heat treatment furnace. The furnace was hermetically sealed and an inert atmosphere was set up inside the latter by means of a continuous purge of high-purity nitrogen (flow rate of 20 l/min). The heat treatment consisted of a heating ramp of 10 K/h followed by a temperature hold at 710° C. (983 K) (0.93 times the melting point T_mof LaBr₃) for 24 hours, then by a cooling ramp of 10 K/h down to ambient temperature. After the treatment, the piece was removed from the crucible and no fracture was visible. The piece was then machined to produce 2″×2″ parts (cylinder having a diameter of 2″ and a height of 2″). No fracture appeared during the machining operations.

EXAMPLE 3

Heat Treatment of an LaCl₃Single Crystal Doped with 10 mol % of Cerium

The melting point of LaCl₃is 860° C. (1133 K). A non-fractured single crystal of LaCl₃:Ce was produced and cooled to ambient temperature. The crystal was placed in a high-purity graphite crucible closed by a high-purity graphite lid. The crucible containing the crystal was then introduced into the heat treatment furnace. The furnace was hermetically sealed and an inert atmosphere was set up inside the latter by means of a continuous purge of high-purity nitrogen (flow rate of 20 l/min). The heat treatment applied consisted of a heating ramp of 10 K/h followed by a temperature hold at 800° C. (1073 K) (0.95 times the melting point of T_mof LaCl₃), for 24 hours, then by a cooling ramp of 10 K/h down to ambient temperature. After the treatment, no fracturing was visible in the single crystal. During the machining no fracture appeared and several 3″×3″ parts were obtained (cylinder having a diameter of 3″ and a height of 3″).

EXAMPLE 4 (Comparative Example)

Machining of a Non-Annealed Crystal of LaBr₃doped with 5 mol % of Cerium

As in the case of Example 2, a single crystal fractured in several large blocks during the growth was used. Examination of the blocks showed that they could be used for producing parts of large volume. No heat treatment was applied to the blocks before their machining. During the machining operations, the appearance of fractures which propagated in the material was observed. The production of large parts was then impossible.

Claims

1-12. (canceled)

13. Single crystal comprising a rare-earth halide that comprises a cleaved surface greater than 5 cm².

14. Single crystal according to claim 13, comprising a cleaved surface greater than 12 cm².

15. Single crystal according to claim 13, wherein it has a hexagonal crystal structure with a P6³/m space group, the cleaved surface corresponding to the crystallographic planes (10 10).

16. Single crystal according to claim 13, wherein the single crystal has a volume greater than 1850 cm³.

17. Single crystal comprising a rare-earth halide that comprises a machined surface greater than 5 cm².

18. Single crystal according to claim 17 comprising a machined surface greater than 12 cm².

19. Single crystal according to claim 17, wherein it has a hexagonal crystal structure with a P6³/m space group, the cleaved surface corresponding to the crystallographic planes (10 10).

20. Single crystal according to claim 17, wherein the single crystal has a volume greater than 1850 cm³.