DE2406008C3 - Transparent gem stone - Google Patents

Description

ι "'= 16 <arc tu

for light falling perpendicularly onto the board, where f '"is the light exit angle, η is the refractive index and» 0 "is the critical angle of total reflection, where 1 denotes the inner angle.

2. Gem according to claim 1, characterized in that that the brilliant graduation decreases as a function of the refractive index Number of corners is chosen with decreasing refractive index.

3. Gem according to claim 1, characterized in that with a refractive index η = about 1.56 a corner number 7. η = about 1.83 a corner number 9, η = about 1.9 to 2 a corner number 9 is selected.

4. Gem according to one of claims 1 to 3, characterized in that in one Back facet angle on the order of 28.5 for a material with a refractive index under 1.7 (glass) a smaller odd number of corners is chosen and the back of the Stone is mirrored in a known manner.

5. Gem according to one of claims 1 to 4, characterized in that the rear facet angle ( ψ) is chosen so that the angle of the light beam with the perpendicular to the rear facet is always greater than the total reflection angle for the material in question and that the number of corners so is chosen that the light exit angle (>'") of the parallel light vector is determined by the refractive index of the transparent material essentially with tg (>', '.') = 1 η.

50

The invention relates to a transparent jewelry case made of a natural or synthetic material with a refractive index π _ 2.2 for a brilliant cut with a girdle, one parallel to it Panel and top and bottom facets. A colored, transparent material is included for you, that occurs naturally or is artificially produced.

The diamond with a conventional iBrillant graduation shows a brilliance that the dtn stone does makes it appear bright, but in which the desired spectral colors are missed. It's already suggested have been to improve this effect in relation to the spectral colors of a diamond, by using an uneven division with a number of corners above 9 for the diamond, in which the angles of inclination of the lower and upper facets in relation to the girdle plane are chosen so that the light reflected by the lower facets and exiting through the upper facets is below an opening angle of the spectrum (opening angle) / f between Γ20 'and 12 57' in relation to the upper facets is scattered. If you transfer such conditions to other materials, then occur geometrically similar to a diamond Gemstones which, however, do not have the brilliance when such a piece is used.

It is also known to have an angle between the girdle plane and the back facets in brilliant shafts between 37 and 45 "to be provided.

From the German patent specification 20 14 966 it has become known to use a rear facet angle smaller than 35 ° for brilliant cuts under certain aspects. This German patent specification is also based on the knowledge that the so-called Auffiederungswinkel [i, which should be large for the fire of the stone, is determined by the angles that are formed by the facets in play when they are side surfaces of an odd-numbered pyramid are. It was also assumed that the exit angle of a light beam from an optically denser material can be at most equal to the feathering critical angle, because the exit angle of the light from an optically dense material determines the feathering angle. For a diamond, a light exit angle of a maximum of 23 56 'and thus a lowering limit angle of 12 57' is given.

In general, it follows from the German patent that according to the choice of the number of corners for one to processing gemstone the angle of inclination of the front and rear facets must be selected, in order to achieve a strong dispersion of the emitting ray of light, so that the gemstone has as much fire as possible. This also resulted in a version with 7 corners that the sum the angle of the anterior and posterior facets to the girdle plane is, for example, 28.4. This condition but does not apply in general, but at most for a diamond, whose fire is in one However, the number of corners is significantly reduced for other reasons.

From British P vntschrift 2 21690 are Gemstones with a division leading to 9 corners are known. If for these gemstones in particular With regard to diamonds, a rear facet angle in the specified range of 38 until 41 is used, this leads to a completely unusable gemstone. In the sense of the Invention, a useful result would only be achieved with a refractive index between 2.28 and 2.13. But no material is known for this. The division 9 = 3x3 is only for ornamental reasons. This known design is suitable neither for the diamond material nor for any other material known material to arrive at a gemstone that can be used for the purposes of the invention.

Materials occur naturally or are synthetically produced and further developed which today are processed with a cut, the Bril from an ornamental point of view The surface finish is imitated, but reflects the light in a modest way, so that the fire is limited is. In the case of such stones, it is desirable, for example, to also have a basic color, e.g. B. of tanzanite, in Blai or to make violet as rich as possible.

The invention is based on the object, too such gemstones aside from diamond, which either have excellent optical properties or a Door permanent use must have the required hardness, to be carried out in such a way that for the respective material a cut in one. Form is used, which in each case has the best possible brilliance with lively Creates fire and changes depending on the material. The specification with a refractive index η <; 2.2 is based on the fact that at η> 2.2 an adjustment in the treated materials is inappropriate because they (like Fabuiii, rutile) have a large play of colors (dispersion of the material).

This object is achieved in that the refractive index of the stone material, the Rear facet angle and an odd brilliant division have a light emission angle of

<arc ι »

20th

for light falling perpendicularly onto the board. Here / "means the light exit angle, η the refractive index and >"' critical angle of total reflection.

The values t each denote the inner angle, ie the angle in the material of the stone at the reflection plane or the exit plane in relation to the normal to this plane.

From this point of view, it is advantageous even with a per se known rear facet angle in the range between 24 and 51.5 ^: to the gondist plane, the facet division or the respective odd brilliant division depending on "the refractive index with a decreasing number of corners with a decreasing refractive index Light exit angle> "is greater than 16 °. The preferred rear facet angle has been selected for reasons of optimum behavior. It is included that it can also be undercut. It can be assumed that in the case of transparent gemstones with 11 g 2.2, the height of the pyramid on the back is not of essential importance. It is preferred that the front facet angle is 7 <33. What is essential, however, is the knowledge that if the area of the rear facet angle remains essentially the same, the number of corners must be changed, specifically as a function of the refractive index. For certain materials it can be provided that with a refractive index η = approximately 1.56 a number of corners 7, η = approximately 1.83 a number of corners 9, η = about 1.9 to 2 a number of corners 9 is selected. In these examples particularly suitable materials are mentioned, in the order of the indications glass, YAG, zirconium. "

As is well known, light oscillates (an electromagnetic wave'i in two vectors, the one for Plane of incidence parallel electric vector and the perpendicular magnetic vector. at

the parallel vector leaves the denser one undamped Material out and with

tg'Ü '= Ii
nnnpHlimnfts into the denser material. When applied to the Brilhni cut, this law leads to an appealing gemstone, since the electrical component is the more essential. At the same time, the opening angle for materials like YAG (with a small dispersion of the material) has become so large that the gemstone allows many individual spectral colors to be recognized.

With a rear facet angle of the order of magnitude of 28.5, a material with a Refractive index π <1.7 (glass) a smaller odd number of corners can be chosen if the back of the Stone is mirrored.

One teaching of the invention, taking into account the above conditions, is that the rear facet angle γ is chosen so that the angle of the light beam with the perpendicular to the rear facet is always greater than the total reflection angle for the material in question and that the number of corners is chosen. that the light exit angle (>"') of the parallel light vector due to the refractive index of the transparent material essentially with te U', ',') = 1 η the exit angle >','.' This leaves the possibility open of changing the rear facet angle, although there is always a dependency on the refractive index and, in turn, the corners are changed depending on the refractive index, under these conditions a cut in glass is also the diamond brilliant similar to / u do.

A characteristic example is the YAG (Yttrium Aluminum Garnet; with a refractive index π = 1.8334 and a dispersion = 0.028 with a Mohs hardness of 8 ¹ _2. In the conventional cut, the YAG diamond shows no spectral colors, but in the new cut it shows With its high hardness of 8 ¹ _{: it} is also suitable for practical use.

It is also noted that the rear facet angle of the cut are critical for all materials because, due to the double reflection on them, the light reaches the table or the front facets by four times the angle of the tolerance of the rear facet angle and there in the event of deviations from the conditions of Invention either receives such a small exit angle that it only appears bright and not colored, or grows over the angle of total reflection and thus remains in the stone. Such a stone looks bland.

It should be noted that total reflection is one of the sharpest limits in optics is. She is to be observed under all circumstances, if a finishing touches the desired success of a strong one Fire should have, in two respects, d. that is, the angles in this regard are intended to go to Reflection on the rear facets larger and the other time to the light emission on the board and front facets smaller than the total reflection angle! being.

The invention is explained below with reference to exemplary embodiments shown in the drawing are shown.

In this shows

F i g. 1 shows a diagram for cuts of gemstones in a coordinate system whose abscissa the number of corners and its ordinate has the light exit angle denser material in air, where certain materials are indicated with their refractive indices and rear facet angles,

F i g. 2 in from FIG. 1 derived diagram in

a coordinate system, the abscissa of which is the refractive index u.:^. ^: c: ~ 7 ordinate the exit angle f angi ^ i,

F i g. 3 a side view of a gemstone,

F i g. 4 a plan view of the gemstone according to FIG. 3,

F i g. 5 shows a diagram for the intensity of the light vectors, shown for the substance YAG as an example.

The F i g. 3 and 4 are only used to explain dimensions. The gemstone has the girdle plane 1. a table 2, so-called front facets 4 and rear facets 5. The rear facet angle 6 is designated with ψ and the front facet angle 7 with < _t . It can be seen that the front and rear facets are offset from one another. F i g. 4 shows that there are seven front facets, so that a heptagonal division is created.

From Fig. 3 it can be seen where the angles Λ ι " and) ■■ '" are assumed according to the above definition, always inside the material and measured to the normal on the assigned plane. Λ and Λ, denote the outer angles, related to the normal of the plane.

The F i g. 1 is derived from the formula

sin (180 / m) sin (ν) = -y- arc tg - (D

in it means

m = number of corners, an odd whole number,
(v) = rear facet angle,
n = refractive index.

If this equation is solved for the rear facet angle or the number of corners m , the values for the most favorable light exit angle result:

tg f ■; = -.

because also applies

sin · W "12) = - arc tg -

where / "'= light exit angle is denser material / air.
It is also included

SlIIi ₀ =

where means

((£ ") = critical angle of total reflection, UZ ') = most favorable light exit angle.

In FIG. 1, the number m of corners is plotted on the abscissa 8 and the light exit angle is plotted on the ordinate 9. With reference to the above formulas, the lines 10, 11, 12 for rear facet angles of 55, 45, 37 ° are then drawn in as parameters. The materials specified in area 13 include glass with a refractive index of 1.56; in the area 14 YAG with the refractive index. 1.8334 and in the area 15 zircon with the refractive index 1.93 to 1.99. An upper value 16, 17, 18 for the light exit angle is drawn in for each area, this being the critical angle for total reflection.

It is also noted that the critical angle of total reflection is obtained if: n (3) is satisfied. ίο If now the most favorable for a certain feature in the area of the selected rear facet angle The corner number is to be determined, the point of intersection between the angle curve and one of the corner numbers corresponding division determined and the intersection according to (3) selected. Result here certain back facet angles on the one hand and certain corner numbers on the other hand, which lead to the lead to the desired result.

For a »diamond-brilliant-like appearance of a cut made of a transparent material is the The rear facet angle is crucial in addition to the odd pitch. This angle is given by the formula (3) determined and must not be exceeded under any circumstances.

A cut made from a transparent material other than diamond is similar to diamond brilliant-cut diamonds it is necessary to make it permanent in use. Glass with a Mohs hardness between 4.5 and 7.0, especially in the soft grades, differs greatly from the diamond, so that it is unavoidable appears to protect the cut stones.

Such protection can be achieved by a layer made of a substance that is much harder to wear than the base body. Such layers can be applied in a high vacuum.
In Fig. 2, the refractive index is indicated in a coordinate system on the abscissa 19 and the inner light exit angle f is indicated on the ordinate 20.

In Fig. 2, the upper curve 26 denotes the angle * ό '\ the critical angle of total reflection, which in the various areas in FIG. Is indicated by the lines 16, 17, 18 1, and the lower curve 27 the angle> ■ '", ie, the best light emission angle, which in Fig. 1 respectively through the lines 31, 32, 33 for the various regions 13, 14 , 15 is indicated.

From Fig. 1 there is the connection with the number of corners, also with reference to a selected rear facet angle, so that from FIG. 1 each can read an area in which particularly favorable conditions are achieved. It can be seen that the ratio between the rear facet angle and the angle of total reflection of the material in question becomes smaller, the smaller the refractive index of the material in question.

Otherwise the rear facets are to be mirrored, as is usual with glass. Glass has a ratio of 1: 1.025. When glass is mirrored on the back is, the ratio of the angles mentioned is infinite. Incident light is reflected from all directions above the girdle plane. Nevertheless the rear facet angle determines the light exit angle according to the above information; for example, glass cuts with 7 corners and 40 ° at 22 in F i g. 1 or with 5 corners and 28.5 ° at 21 in FIG. 1 the same exit angle of (/ ") = 32.6 °.

The following materials are specified, for example:

Malcruil HrcchiimiNinuex Angle tic. ToImI- rellcvion Zircon 1.93-1.99 30 39 ' YAG (yttrium 1,833 33 "3 ' Aluminum garnet) (syn thetic) Monticellite 1.79-1.84 33 "3O ' corundum 1.76-1.77 34'30 ' Feldspar 1.52-1.53 4054 ' Tanzanite Glass 1.50 41 48 ' Glass 1.90 3Γ45 '

The refractive index of YAG is η = 1.8334.
For the angle of incidence / = 0 ', the following applies:

/H

⁼ U

f I 4 /)

X.65% . = - 91.35% .

The critical angle of total reflection is <ό "= aresin (1π) = 33.05 °.

This corresponds to point 29 in FIG. 2. Correspondingly For other materials, points 28 zirconia door and 30 for glass result.

The other values in the diagram were calculated using Fresnel's formulas:

r = lg ² {ι - ΛΙ / tg ² (; + Λ),
r = sin ² (/ - ΛΙ / sin ² (, + D),

In Fig. 1, the rear facet angle is for glass of 28.5 "at location 21 and the back facet angle of 40 ° at location 22 at line 31, the the area 13 delimits downward. The best light exit angle is then on line 31 Ordinate 9 can be read off.

The corresponding line for the area 14, YAG, is designated by 32 and intersects the ordinate 9 at the light exit angle> ■ '" by 28.6 °. This results in a rear facet angle of 46.5" at the point 23. The point 24 in the area 15, zirconium, denotes the rear facet angle 42.8 °, with the exit angle r ′ ″ at the intersection of the line 33 and the ordinate 9 being readable with the selected number of corners.

In Fig. j the special conditions for the material YAG are now explained in particular. F i g. 5 practically contains two diagrams which are plotted from an abscissa 34 on which, in accordance with the division on the line 35, an internal angle of incidence r of 0 to 90 °. The ordinate section 36 contains from the abscissa 34 upwards from 0 to 100 the percent of the reflectance r at the air / material interface, ie in the present case YAG, and the section 37 from top to bottom from 100 to 0% the values of the permeability d an the air / material interface, ie YAG and at the material / air interface with the abscissa 38; because the light exit angle>'"is indicated on the abscissa 38.

The values for the degree of reflection r and transmittance d are each designated as follows, although the component decomposition is also given in that r "and d" represent the components of the vectors r and d parallel to the entry and exit planes, while the curves r, and d, the components of the vectors perpendicular to the planes.

The diagram shows the degree of reflection r and the transmittance d over the angle of incidence r according to Fresnel's formulas for the material YAG (Yttrium Aluminum Garnet).

r ,, + r.

d d

sin2 (O sin2 [D) ι sin ² l · 4- .1) cos ² (; -D).
sin2 (/) sin 2 <A) .sin ² (, + D).

It follows from FIG. 3 that Λ is the outer perpendicular angle of incidence.

For the material YAG, it follows from FIG. 5 that at the point of incidence angle _f = arc tg η = 61.39 ° the parallel component of the light enters the material unhindered, the degree of reflection being 0 and the transmittance being 100%. As can be seen from the line 38, this corresponds to the light exit angle r '" = 28.61 °. For the area 14 in FIG. 1 for the material YAG, this corresponds to the intersection of the line 32 with the ordinate 9, so that 1 shows how an advantageous cut can be selected as a function of the number of corners and the rear facet angle.

Through the in F i g. The component decomposition shown in FIG. 5 can be used to determine the most favorable operating point for the respective material by touching the curves r 1 and d 1 with the abscissa 34, the values being determined using the specified formulas. In the case of the inner exit angle of 28.61 °, according to FIG. 3, there is a maximum opening angle on the outside, 1

The lines 31, 32, 33 in FIG. 1 each show the position of the maximum working point, with compliance of the working point, other values such as rear facet angle and number of corners are dependent on each other are changeable.

F i g. 5 explains the relationships for one material, namely for YAG. Corresponding curves can be set up for other materials. The components r "and d" are particularly essential for the in FIG. 3 also shown Auffiederungswinkel ß.

For this purpose 4 sheets of drawings

609 639/285

Claims (1)

Patent claims: 1. Transparent gemstone made of a natural or synthetic material with a refractive index η _: 2.2 in a brilliant cut with a Girdle, a panel parallel to it and upper and lower part facets, characterized in that that the refractive index of the stone material. the back facet angle and an odd one Brilliant graduation has a light emission angle of