Preparation of alpha-alumina in supercritical fluids

Abstract

The present invention relates to a process for preparing a-alumina in a supercritical fluid, to a-alumina and a-alumina particles obtainable by said process.

Description

[Technical field]

[0001] The present invention relates to a process for preparing alpha-alumina in a supercritical fluid, to alpha-alumina and alpha-alumina particles obtainable by said process. [Background technology]

[0002] Alumina (aluminum oxide, Al2O3) is known to occur in metastable phases, including γ-alumina, δ-alumina, θ-alumina, and α-alumina. α-alumina, also known as corundum, is the most thermodynamically stable phase of alumina. α-alumina has many applications due to its stability, including its high melting point, hardness, and resistance to attack by strong inorganic acids. One such application is the use of α-alumina in abrasives and refractories. There are various forms of naturally occurring alpha-alumina, including some gemstones that may be colored due to impurities present in the corundum crystal. Alpha-alumina can also be synthesized using methods such as flame fusion, flux solution, and hydrothermal synthesis. All of the known methods present challenges including high levels of energy use, high cost, and difficulty in controlling the morphology and / or homogeneity of the product. It is therefore desirable to provide an alternative method for preparing α-alumina that addresses the shortcomings of known synthetic methods. Summary of the Invention

[0003] The invention is defined in the appended claims. According to a first aspect, there is provided a method for preparing alpha alumina, comprising the steps of: (a) providing an aluminum precursor; (b) mixing an aluminum precursor with a base in a solvent; (c) aging the mixture of step (b) until the aluminum precursor dissolves; (d) A method is provided which comprises treating the solution of (c) at a temperature and pressure above the critical point of the solvent used. According to a second aspect, there is provided α-alumina obtainable according to the method of the first aspect. According to a third aspect, there is provided α-alumina particles having a polyhedral morphology. Certain embodiments of the present invention provide the following advantages: The desirable ease of synthesis of α-alumina, - favorable composite cost, The desired conversion to a single form of alumina, i.e. alpha-alumina, - The desired morphology of α-alumina, - desirable homogeneity of α-alumina particles, - the desired particle size of the α-alumina particles; -Desirable low-temperature synthesis may provide one or more of:

[0004] The details, examples and preferences set forth in relation to any particular one or more of the stated aspects of the invention apply equally to all aspects of the invention. Any combination of the embodiments, examples and preferences described herein is encompassed by the invention in all possible variations thereof, unless otherwise indicated herein or clearly contradicted by context. The invention is further illustrated by reference to the following figures. [Brief description of the drawings]

[0005] [Figure 1] FIG. 1 is a diagram of an example of an apparatus used to prepare α-alumina. [Diagram 2] FIG. 2 is an XRD diagram of the product from Example 1. [Figure 3a] FIG. 3 is an SEM of the product from Example 1 shown in both FIG. 3a and FIG. 3b. [Figure 3b] FIG. 3 is an SEM of the product from Example 1 shown in both FIG. 3a and FIG. 3b. [Figure 4]FIG. 2 is an XRD diagram of the product from Example 2. [Figure 5a] FIG. 5 is an SEM of the product from Example 2 shown in both FIG. 5a and FIG. 5b. [Figure 5b] FIG. 5 is an SEM of the product from Example 2 shown in both FIG. 5a and FIG. 5b. [Figure 6] FIG. 1 is an XRD diagram of the product from Example 3. [Figure 7] FIG. 1 is an XRD diagram of the product from Example 4. [Figure 8] FIG. 1 is an XRD diagram of the product from Example 5. [Figure 9] FIG. 1 shows the measured permeability of aged (unmature solution) and aged (mature solution) mixtures of Example 1. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0006] It will be understood that the following description and references to the figures relate to exemplary embodiments of the invention and are not intended to limit the scope of the claims. The present invention is based on the surprising discovery that α-alumina can be efficiently prepared using the methods disclosed herein. The present invention utilizes supercritical fluids (SCFs) to obtain α-alumina, which has not been shown to be successful in the art. SCFs are substances that do not have distinct liquid and gas phases at temperatures and pressures above their critical point. For example, the density of SCFs is about 200-400 times that of the gaseous state, and thus can be similar to the liquid state. However, the viscosity of SCFs is similar to that of the gaseous state. Furthermore, the diffusion coefficient of SCFs is lower than that of gases, but higher than that of liquids. Critical points are specific to each substance. For example, for water, the critical temperature (T c ) is 647 K, and the critical pressure (p c ) is 221 bar. It has been found that when applying the method of the present invention, an aluminum precursor is mixed with a base in a solvent, followed by aging and treatment above the critical point of the solvent, to obtain α-alumina.

[0007] In some embodiments, the aluminum precursor is selected from aluminum nitrate, aluminum sulfate, aluminum chloride, or a combination thereof. In some examples, the aluminum precursor is aluminum nitrate. In some examples, the aluminum precursor is aluminum sulfate. In some examples, the precursor is aluminum chloride. The aluminum precursor may be used in combination with a solvent. In some embodiments, the solvent is selected from water, ethanol, methanol, or a combination thereof. In some examples, the solvent is water. In some examples, the solvent is ethanol. In some examples, the solvent is methanol. In some embodiments, the aluminum precursor in the solvent has a concentration of about 0.2 M. For example, the aluminum precursor in the solvent has a concentration of about 0.001 M to about 7.5 M. In some examples, the aluminum precursor has a concentration of about 0.005 M to about 7.0 M, or about 0.01 M to about 6.5 M, or about 0.05 M to about 6.0 M, or about 0.1 M to about 5.5 M, or about 0.5 M to about 5.0 M, or about 1.0 M to about 4.5 M, or about 1.5 M to about 4.0 M, or about 2.0 M to about 3.5 M, or about 2.5 M to about 3.0 M.

[0008] In some examples, the solvent is water and the aluminum precursor in the water has a concentration of about 0.005M to about 7.0M, or about 0.01M to about 6.5M, or about 0.05M to about 6.0M, or about 0.1M to about 5.5M, or about 0.5M to about 5.0M, or about 1.0M to about 4.5M, or about 1.5M to about 4.0M, or about 2.0M to about 3.5M, or about 2.5M to about 3.0M.

[0009] In some examples, the solvent is methanol and the aluminum precursor in the methanol has a concentration of about 0.005M to about 7.0M, or about 0.01M to about 6.5M, or about 0.05M to about 6.0M, or about 0.1M to about 5.5M, or about 0.5M to about 5.0M, or about 1.0M to about 4.5M, or about 1.5M to about 4.0M, or about 2.0M to about 3.5M, or about 2.5M to about 3.0M.

[0010] In some examples, the solvent is ethanol and the aluminum precursor in the ethanol has a concentration of about 0.005M to about 7.0M, or about 0.01M to about 6.5M, or about 0.05M to about 6.0M, or about 0.1M to about 5.5M, or about 0.5M to about 5.0M, or about 1.0M to about 4.5M, or about 1.5M to about 4.0M, or about 2.0M to about 3.5M, or about 2.5M to about 3.0M. At 100°C, aluminum nitrate is soluble in water (160 g / 100 mL), ethanol (8.63 g / 100 mL), and methanol (14.45 g / 100 mL). At 20°C, aluminum nitrate nonahydrate has a solubility of (67 g / 100 mL). For example, aluminum nitrate has a maximum concentration of 7.5 M in water, 0.41 M in ethanol, and 0.68 M in methanol. Aluminum sulfate is soluble in water (2.71 g / mL) and is sparingly soluble in alcohol. Aluminum chloride is soluble in water and ethanol.

[0011] In some embodiments, the base is selected from sodium hydroxide, potassium hydroxide, urea pyridine, methylamine, imidazole, histidine, guanidine, or a combination thereof. In some embodiments, the base is selected from sodium hydroxide, potassium hydroxide, or a combination thereof. In some examples, the base is sodium hydroxide. In some examples, the base is potassium hydroxide. In some embodiments, the base may be used in combination with a solvent. In some embodiments, the solvent is selected from water, ethanol, methanol, or a combination thereof. In some examples, the solvent is water. In some examples, the solvent is ethanol. In some examples, the solvent is methanol. In some examples, the solvent mixed with the aluminum precursor is the same solvent mixed with the base.

[0012] In some embodiments, the base is mixed with water and the basic solution has a concentration of 0.5M. For example, the base has a concentration of about 0.0025M to about 18.75M. In some examples, the aluminum precursor has a concentration of about 0.0125M to about 17.5M, or about 0.025M to about 16.25M, or about 0.125M to about 15.0M, or about 0.25M to about 13.75M, or about 1.25M to about 12.5M, or about 2.5M to about 11.25M, or about 3.75M to about 10.0M, or about 5.0M to about 8.75M, or about 6.25M to about 7.5M. For example, the ratio of base to water is about 1:2.0 to 1:3.0. For example, the ratio of base to water is 1:2:5. In some embodiments, the mixing step (b) is carried out at a temperature of about 20° C. to about 100° C. For example, the mixing step (b) is carried out at a temperature of about 20° C. to about 90° C., or about 20° C. to about 60° C., or about 20° C. to about 40° C., or about 20° C. to about 30° C., or about 25° C. to about 30° C. For example, the mixing step (b) is carried out at a temperature of about 30° C. to about 90° C., or about 40° C. to about 80° C., or about 50° C. to about 70° C., or about 55° C. to about 60° C.

[0013] In some embodiments, the solution of aluminum precursor after completion of step (c) has a pH of about 4 to about 6. For example, the pH of the dissolved aluminum precursor after completion of step (c) is about 4.5, or about 5, or about 5.5. In some embodiments, the mixture in step (c) is stirred at a speed of about 20 rpm to about 1500 rpm. For example, the mixture in step (c) is stirred at a speed of about 50 rpm to about 1450 rpm, or at a speed of about 100 rpm to about 1400 rpm, or at a speed of about 300 rpm to about 1300 rpm, or at a speed of about 500 rpm to about 1100 rpm, or at a speed of about 700 rpm to about 900 rpm, or at a speed of about 500 rpm.

[0014] In some embodiments, step (c) is carried out at a temperature of about 25° C. to about 100° C. For example, step (c) is carried out at a temperature of about 25° C. to about 75° C. In some embodiments, step (c) is carried out for at least 0.5 hours. For example, step (c) is carried out for at least about 1 hour, or about 2 hours, or about 2.5 hours, or about 3 hours, or about 3.5 hours, or about 4 hours, or about 4.5 hours, or about 5 hours, or about 5.5 hours, or about 6 hours. In some embodiments, step (c) is carried out for at least 2 hours at 25° C. For example, step (c) is carried out at 25° C. for at least about 3 hours, or about 3.5 hours, or about 4 hours, or about 4.5 hours, or about 5 hours, or about 5.5 hours, or about 6 hours.

[0015] In some embodiments, step (c) is carried out for at least 2 hours at 50° C. For example, step (c) is carried out at 25° C. for at least about 3 hours, or about 3.5 hours, or about 4 hours, or about 4.5 hours, or about 5 hours, or about 5.5 hours, or about 6 hours. In some embodiments, step (c) is carried out for at least 2 hours at 75° C. For example, step (c) is carried out at 25° C. for at least about 3 hours, or about 3.5 hours, or about 4 hours, or about 4.5 hours, or about 5 hours, or about 5.5 hours, or about 6 hours. In some embodiments, step (c) is carried out for at least 2 hours at 100° C. For example, step (c) is carried out at 25° C. for at least about 3 hours, or about 3.5 hours, or about 4 hours, or about 4.5 hours, or about 5 hours, or about 5.5 hours, or about 6 hours.

[0016] In some embodiments, step (c) is aged until the mixture is clear. The determination of whether the mixture is clear can be performed using any known method. For example, the delta back scattering number can be used to determine the transparency. If the delta back scattering number is negative, the solution is clear. If the delta back scattering number is positive, the solution is cloudy. In some examples, a Turbiscan Lab instrument available from Formulaction can be used. The mixture is considered to be clear if the transmittance measured by the Turbiscan Lab instrument is at least 80%, such as at least 83%, preferably at least 85%. In some examples, the transparency of the mixture can be determined by DIN ISO 18748. In some embodiments, step (d) is carried out in a high temperature mixing reactor. An example of a high temperature mixing reactor is depicted in FIG. 1. In some embodiments, the temperature used in step (d) is about 400° C. to about 1000° C. For example, the temperature used in step (d) is about 420° C. to about 950° C., or about 440° C. to about 900° C., or about 450° C. to about 850° C., or about 460° C. to about 800° C., or about 480° C. to about 700° C., or about 500° C. to about 650° C., or about 550° C. to about 600° C. In some examples, the temperature used in step (d) is about 450° C. to about 500° C. In some embodiments, the pressure used in step (d) is from about 10 bar to about 500 bar. For example, the pressure used in step (d) is from about 25 bar to about 450 bar, or from about 50 bar to about 400 bar, or from about 100 bar to about 350 bar, or from about 150 bar to about 300 bar, or from about 200 bar to about 250 bar, or from about 230 bar to about 500 bar.

[0017] In some embodiments, step (d) is carried out in a reactor at the temperature and pressure for a time period between about 0.5 milliseconds and about 50 days. For example, step (d) is carried out in a reactor at the temperature and pressure for a time period between about 10 milliseconds, about 100 milliseconds, about 500 milliseconds, about 1 second, about 10 seconds, about 30 seconds, about 1 minute, about 30 minutes, about 1 hour, about 6 hours, about 12 hours, about 18 hours, about 1 day, about 5 days, about 10 days, about 15 days, about 20 days, about 25 days, about 30 days, about 35 days, about 40 days, about 45 days, or about 50 days.

[0018] In some embodiments, α-alumina particles in polyhedral morphology are provided. The inventors of the present invention have surprisingly found that a controlled morphology of α-alumina particles can be obtained with respect to the shape of the α-alumina particles. In some embodiments, the morphology of the α-alumina particles can be controlled in relation to the percentage of polyhedrons formed relative to the total amount of particles formed. In some embodiments, the α-alumina particles in polyhedral morphology constitute about 10% of the entire sample, or up to about 20% of the entire sample, or up to about 30% of the entire sample, or up to about 40% of the entire sample, or up to about 50% of the entire sample, or up to about 60% of the entire sample, or up to about 70% of the entire sample, or up to about 80% of the entire sample, or up to about 90% of the entire sample, or up to about 95% of the entire sample, or up to about 99% of the entire sample, or up to about 100% of the entire sample.

[0019] In some embodiments, the polyhedrons of the α-alumina particles have at least 12 faces, or at least 13 faces, or at least 14 faces, or 12 faces, or 13 faces, or 14 faces, or 15 faces, or 16 faces. In some embodiments, the polyhedron is a hexagonal bipyramid. In some embodiments, the polyhedron is a truncated hexagonal bipyramid. A truncated hexagonal bipyramid is commonly known as a hexagonal bipyramid with two additional vertices opposite each other that have been truncated to form two additional faces. In some embodiments, the polyhedron is a truncated hexagonal bipyramid according to FIG. 3a or FIG. 3b.

[0020] In one embodiment, the method according to the present invention has the following effects: - Increased preparation efficiency, - A decrease in the pressure used in the process, - A reduction in the temperature used in the process, - the reduction of the temperatures used in the process compared to conventional thermal processes such as melting or calcination; - Increased product purity, - Good control of morphology, - Good homogeneity of the product The present invention may have one or more of the following:

[0021] The present disclosure may be described by one or more of the following paragraphs. 1. A method for preparing alpha alumina comprising the steps of: (a) providing an aluminum precursor; (b) mixing an aluminum precursor with a base in a solvent; (c) aging the mixture of step (b) until the aluminum precursor dissolves; (d) treating the solution of (c) at a temperature and pressure above the critical point of the solvent used. 2. The method according to paragraph 1, wherein the aluminum precursor is selected from aluminum nitrate, aluminum sulfate, aluminum chloride, or a combination thereof. 3. The process according to paragraph 1 or 2, wherein the solvent is selected from water, ethanol, methanol or a combination thereof. 4. The process according to any one of paragraphs 1 to 3, wherein the base is selected from sodium hydroxide, potassium hydroxide, or a combination thereof. 5. The process according to any one of paragraphs 1 to 4, wherein the solvent is water. 6. The process according to any one of paragraphs 1 to 5, wherein the mixing step in step (b) is carried out at a temperature of from about 20°C to about 100°C. 7. The method according to any one of paragraphs 1 to 6, wherein the pH of step (c) is from about 4 to about 6. 8. The method according to any one of paragraphs 1 to 7, wherein step (c) is carried out at a temperature of from about 25° C. to about 100° C. 9. The process according to any one of paragraphs 1 to 8, wherein the mixture of step (c) is stirred at a speed between 20 rpm and 1500 rpm. 10. The method according to any one of paragraphs 1 to 9, wherein step (c) is carried out for at least 0.5 hours. 11. The method according to any one of paragraphs 1 to 10, wherein step (c) is aged until the mixture becomes clear. 12. The method according to paragraph K, in which the transparency of the mixture is determined according to DIN ISO 18748. 13. The method according to any one of paragraphs 1 to 12, wherein the temperature used in step (d) is from about 400°C to about 1000°C and the pressure used in step (d) is from about 10 bar to about 500 bar. 14. The method according to any one of paragraphs 1 to 13, wherein the temperature used in step (d) is from about 400°C to about 700°C and the pressure used in step (d) is from about 230 bar to about 500 bar. 15. The method according to any one of paragraphs 1 to 14, wherein the reactor processes the reactants at said temperature and said pressure for a time period from 5 milliseconds to 50 days. 16. α-alumina obtainable according to the process of any one of paragraphs 1 to 15. 17. α-alumina particles of polyhedral morphology. 18. The α-alumina particles of paragraph 17, wherein the polyhedrons have at least 12 faces. 19. The α-alumina particles of paragraphs 17 or 18, wherein the polyhedrons are hexagonal bipyramids. 20. The α-alumina particles of paragraphs 17 or 18, wherein the polyhedrons are truncated hexagonal bipyramids. EXAMPLES

[0022] The apparatus used to prepare α-alumina is depicted in Figure 1, which is a schematic diagram and is described below. In addition to showing general details of the apparatus, specific details of the apparatus used in the examples disclosed herein are also shown.

[0023] As seen in FIG. 1, two high pressure pumps (JASCO PU-4086) are used to circulate the fluids under pressure through the process. The operating pressure in the following examples is 250 bar. The pressure is maintained in the process by using a back pressure regulator (Swagelok BSN2-02-5-VVK). The water was heated through a tube that went into a furnace (CERADEL Industries PTF 12 / 105 / 500). The tube that went into the furnace (HP1 to reactor) was made of Hastelloy C-276, had a length of 12 m and an outer diameter of 1 / 8 inch. The injection tube (HP2 pump to reactor) was made of stainless steel 316L. The reactor consisted of a 1 / 8 inch Tee made of SS316L from Swagelok. The product is formed when supercritical water is mixed with the precursor solution. The slurry is then cooled in a chiller consisting of a parallel flow heat exchanger (slurry circulates through ⅛ inch SS316L tubing and cooling water circulates through ½ inch SS316L tubing). Once the slurry is cooled, it is passed through a back pressure regulator where the pressure is reduced to atmospheric pressure.

[0024] Method 1 A solution of 0.2 M of aluminum nitrate (Al(NO3)3.9H20, Alfa Aesar) in 200 mL of water is prepared, and a solution of 0.5 M of base (B) in 200 mL of water is prepared. Once both precursors are dissolved in their respective beakers, the solution of base (B) is added to the aluminum nitrate solution under stirring (500 rpm). The resulting solution is then aged under stirring for a specific time (aging time, AT).

[0025] Using the reactors disclosed in FIG. 1 in series, distilled water is introduced into the process through the HP1 and HP2 pumps with a flow of 20 mL / min at HP1 and 7 mL / min at HP2. When the water flows out through the back pressure regulator (BPR), the pressure is gradually increased to 250 bar by squeezing the BPR. The pressure in the process is set to the working pressure (250 bar) and the temperature of the furnace is set to a predetermined temperature (furnace temperature, FT). Once the temperature and pressure have stabilized, the measured temperature after the reactor (temperature after furnace, AFT) is measured and when this temperature is reached, the previously prepared and aged solution is fed to the HP2 pump. The flow rate at HP1 is 20 mL / min and at HP2 is 7 mL / min. The solution of the precursor is then continuously injected into the process and the resulting material is continuously collected after the BPR. Once the entire solution has passed through the process, the process is stopped and the resulting material is collected in a beaker.

[0026] The collected slurry is then centrifuged to collect the solids, which are washed five times by adding the same volume as was removed in each step followed by repeating the centrifugation steps. Once these steps are complete, the sample is dried in an oven at 200° C. and then characterized by X-ray diffraction (XRD) and / or scanning electron microscopy (SEM). XRD and SEM may be performed by any known method.

[0027] XRD measurements are obtained by the following method: A sample of particles is ground to a particle size of less than 10 μm (by sedigraph). A lump-free powder is produced and inserted into the XRD sample holder by packing using a suitable method to ensure that preferred orientation is avoided. The sample is scanned by XRD (e.g. D8 Advance A25, Bruker, Bragg-Brentano type and K430 X-ray generator). CuK α1α2(λ1=1.54060 Å, λ2=1.54439 Å) lines are generated at 40 kV and 45 mA, from 2θ=5° to 2θ=80°, using a step size of 0.0019°. Scans are viewed with XRD analysis software HighScore Plus (available from Malvern Panalytical) or DIFFRAC.EVA (available from Bruker), and XRD peaks are assigned according to the PDF-2 minerals database (available from the International Centre for Diffraction Data). XRD peak information is also available from public databases (such as the Mineralogy Database at http: / / webmineral.com). The amount of each mineral in the sample is determined from the height of the corresponding XRD peak by the Reference Intensity Ratio (RIR) method. In this example, Malvern Panalytical's X'Pert PRO was used.

[0028] In this example, the obtained product was observed with a scanning electron microscope (FEI Quanta Feg 250). Example 1 was carried out to obtain Example Numbers (Ex. No.) 1 to 5 as shown in Tables 1 and 2. Ex. Nos. 1, 2, 4, and 5 are according to the invention. Ex. No. 3 is a comparative example where no base was used. As can be seen from the results in Table 2, the examples according to the invention result in the formation of α-alumina with homogeneous morphology and particles according to the invention. The ageing of the mixture was monitored by Turbiscan and the ageing time was set up so that the transparency of the mixture was at least 80%.

[0029] The permeability measured for the mixture of Example 1 after 5 minutes of aging (unmature solution) and after 70 hours of aging (mature solution) is shown in Figure 9. At 5 minutes the permeability was less than 10%, while at 70 hours the permeability was about 87%.

[0030] [Table 1]

[0031]

Table 2

Claims

1. 1. A process for preparing alpha alumina comprising the steps of: (a) providing an aluminum precursor; (b) mixing an aluminum precursor with a base in a solvent; (c) aging the mixture of step (b) until the aluminum precursor dissolves; (d) treating the solution of (c) at a temperature and pressure above the critical point of the solvent used.

2. The method of claim 1 , wherein the aluminum precursor is selected from aluminum nitrate, aluminum sulfate, aluminum chloride, or a combination thereof.

3. 3. The process according to claim 1 or 2, wherein the solvent is selected from water, ethanol, methanol or a combination thereof, preferably the solvent is water.

4. The process of any one of claims 1 to 3, wherein the base is selected from sodium hydroxide, potassium hydroxide, or a combination thereof.

5. The method of any one of claims 1 to 4, wherein the mixing in step (b) is carried out at a temperature of from about 20°C to about 100°C.

6. The method of any one of claims 1 to 5, wherein the pH of step (c) is from about 4 to about 6.

7. The method of any one of claims 1 to 6, wherein step (c) is carried out at a temperature of from about 25°C to about 100°C.

8. The method of any one of claims 1 to 7, wherein the mixture of step (c) is stirred at a speed of from 20 rpm to 1500 rpm.

9. The method of any one of claims 1 to 8, wherein step (c) is carried out for at least 0.5 hours.

10. 10. The method of any one of claims 1 to 9, wherein step (c) is aged until the mixture is transparent, the clarity being determined by DIN ISO 18748.

11. 11. The method of any one of claims 1 to 10, wherein the temperature used in step (d) is from about 400°C to about 1000°C or from about 400°C to about 700°C and the pressure used in step (d) is from about 10 bar to about 500 bar or from about 230 bar to about 500 bar.

12. 12. The method of any one of claims 1 to 11, wherein the reactor processes the reactants at said temperature and said pressure for a time period between 5 milliseconds and 50 days.

13. α-alumina obtainable according to the method according to any one of claims 1 to 12.

14. Alpha-alumina particles in the form of polyhedra, the polyhedra having at least 12 faces.

15. 15. The α-alumina particles of claim 14, wherein the polyhedrons are hexagonal bipyramids or truncated hexagonal bipyramids.

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