Crystal biaxial, negative

FIGURE 5.10. (c) A biaxial negative orthorhombic crystal in which [for convenience, in this case], X = c, Y = a, and Z = b. The optic plauie is parallel to (100). ((a), (h) and (c) courtesy Ernest E. Wahlstrom and John Wiley k, Sons, Inc. From Wahlstrom, E. E. Optical Crystallography. 5th edn. John Wiley. New York, Chichester, Brisbane, Toronto (1979). John Wiley Sons, Inc.). ... 

Methylgermanium triiodide is a lemon-yellow solid (m.p. 48.5°). Its crystals are anisotropic, biaxial negative, and probably rhombohedral. It is thermally stable, and may be distilled with no evidence of decomposition (b.p. 237° at 752 mm). The color dfeepens to red as the temperature rises, but returns to yellow as the sample cools. It is soluble in water with extensive hydrolysis, and is ammonolyzed in liquid ammonia. It is soluble in organic solvents and may be recrystallized from petrolevim ether by cooling a solution, saturated at 50°, to —33° by means of a bath of liquid ammonia. It may be sublimed at 45° in a vacuum to give beautiful, large, clear yellow crystals. 

Disodium dihydrogen pyrophosphate dissolves slowly in cold water, a 1 per cent solution having a pH of 4.1 to 4.3. One hydrate, Na2H2P207 6Ha0, can be crystallized from aqueous solutions at slightly below room temperature. The hydrated crystals are biaxial negative with a = 1.456, jS = 1.464, and 7 = 1.465( .002). When heated they lose their water of crystallization around 36°. In aqueous solution the disodium pyrophosphate hydrolyzes to orthophosphate, the rate of hydrolysis depending on the temperature. At 70° a 1 per cent solution is hydrolyzed approximately 10 per cent in 6 hours at 100° the hydrolysis is complete in less than 6 hours. ... 

When anhydrous disodium dihydrogen p3Tophosphate is prepared by the acetic acid method, the product is sufficiently crystalline for optical measurements. The crystals are orthorhombic pyramids, biaxial negative with a = 1.501 . 002, 8 = 1.514 . 005, and 7 = 1-522 . 002. Ingerson and Morey give a = 1.510 and 7 = 1.517 for very fine needle crystals. 

Anhydrous sodium trimetaphosphate is crystalline and water-soluble, but has no calcium-sequestering value. The trimetaphosphate is not precipitated by zinc, silver, or barium ions. Slow hydrolysis occurs in aqueous solution to give orthophosphate ions with intermediate formation of triphosphate ions. Conversion to triphosphate occurs very rapidly when the trimetaphophate is heated for a few minutes at 100° in the presence of an excess of sodium hydroude. No satisfactory quantitative method for its determination has been reported. It can, however, be identified by its refractive indexes, since the crystals are biaxial negative with a = 1.471, jS = 1.476, y = 1.480 ( .002). 

Crystals of the 6-hydrate, NajPj09-6H20, are triclinic rhombohedra, biaxial negative Avith a = 1.433, jS = 1.442, and y = 1.446 ( .002). These crystals are efflorescent at room temperature, lose water rapidly at 50°, and melt in their water of crystallization if heated rapidly to around 63°. 

Finally, phase biaxiality has been studied by dissolving deuterated solute molecules in discotic liquid crystals [3.32]. Since discotic liquid crystals have negative Ax, an aligned sample consisting of one type of deuteron will exhibit a planar powder pattern (Fig. 3.7) without the necessity of sample rotation as in the conventional rod-like liquid crystals. Two discotic phases, Drd and have been studied by spectral pattern simulation using nonzero [3.32]. 

Another example of a symmetry change is the field-induced biaxiality in nematic liquid crystals with negative dielectric anisotropy [29]. In this case the field is applied perpendicular to the director. The latter is parallel to the z axis. The orientational order at a point r in a nematic liquid crystal is defined by the ordering matrix... 

The Fedorov complex symbol is 4a(45° 36 ) 0. Optically the crystals are biaxial the acute bisectrix is negative. 

Interference figures These will indicate whether the crystal is optically positive or negative and, if biaxial, the angle between the optic axes. 

Birefringence The difference between the refractive index for the extraordinary and ordinary rays (he — no) in a uniaxial or biaxial crystal. If a crystal, such as quartz, is positively birefringent, no is less than ns, and the velocity of the ordinary-ray is greater than that of the extraordinary ray. The reverse is true for a negatively birefringent crystal. 

Negative crystals n. A uniaxial crystal is optically negative if < to. A biaxial crystal is said to be optically negative if... 

Sign of double refraction n. An empirical classification of crystals it is positive for uniaxial crystals when s > o), for biaxial crystals when y — > J — a. It is negative... 

For biaxial crystals, the optical indicatrix is a bilayer surface with four points of interlayer contact, which correspond to the directions of the two optical axes. In the simple case of light propagation in the principal planes XY, YZ, and XZ, the dependences of the refractive indices on the direction of light propagation are represented by a combination of an ellipse and a circle. Thus, in the principal planes, a biaxial crystal can be considered as a uniaxial crystal for example, a biaxial crystal with nz > ny > nx in the XY plane is similar to a negative uniaxial crystal with Ho=nz... 

Usually the z axis, sometimes also referred to as the crystal axis, is chosen as an axis of symmetry. For light propagating along this axis of symmetry, since hght is a transverse electromagnetic wave, its polarization vector (defined by the direction of its electric field E) is perpendicular to the z axis, that is, E lies on the x-y plane. If U] and 2 are unequal, such crystal is usually called biaxial. On the other hand, if = 2 (for all intents and purposes), the crystal is called uniaxial. Conventionally, if n > n, 2, the crystal is referred to as positive uniaxial or biaxial, whereas if n is < i, 2, the crystal is referred to as negative uniaxial or biaxial. 

Orthorhombic, monoclinic and triclinic crystals are biaxial, while tetragonal, hexagonal and rhombohedral crystals are uniaxial. For uniaxial crystals, the principal axis that exhibits the anisotropy is called the optic axis. The crystal is positive uniaxial if > and negative uniaxial if < e. 

Biaxial, uniaxial, as well as isotropic 3D ordering were detected for various orientations of azochromophores and classified by analogy to crystal optics as positive and negative C and A plates [36],... 

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