ON THE CHARACTERISTIC TEMPERATURES OF SINGLE CRYSTALS AND THE DISPERSION OF THE "DEBYE HEAT WAVES”

1953 ◽  
Vol 31 (1) ◽  
pp. 112-119 ◽  
Author(s):  
E. J. Post
Keyword(s):  
Single Crystal ◽  
Single Crystals ◽  
Elastic Constants ◽  
Heat Waves ◽  
Lattice Structure ◽  
Characteristic Temperature ◽  
Normal Modes ◽  
Simple Calculation ◽  
Characteristic Temperatures ◽  
Elastic Data

A procedure for the calculation of the number of normal modes of a single crystal is proposed which takes an intermediate position between the methods of Debye and Born–von Karman. The method of Debye is extended to an anisotropic continuum, where the cutoff and dispersion phenomena, which are due to the lattice structure, are accounted for in a semiempirical way. It appears possible to define a finite number of characteristic temperatures (one for cubic crystals and at most three for crystals of low symmetry) independent of direction. This ensures a comparatively simple calculation from the phenomenological elastic constants of the crystal, as such retaining one of the pleasing features of Debye's theory, i.e., a straightforward correlation between thermal and elastic data.The method is applied to eight cubic monatomic crystals for which elastic data are available. The results provide some additional evidence to emphasize the significance of the dispersion of the Debye heat waves.An application to the hexagonal crystals of cadmium and zinc leads to results similar to those obtained by Grüneisen and Goens who produced with these crystals the first experimental evidence of the dispersion phenomenon using the concept of a characteristic temperature dependent on direction.In the last section the correlation between the elastic constants of single crystals and the corresponding quasi-isotropic materials is discussed and illustrated with data found in the literature. It is shown that the polycrystalline state is more "elastic" (sometimes very considerably) than the single crystal state. The consequences of this "boundary layer elasticity" for the calculation of θ values are discussed.

Debye Characteristic Temperatures of Cubic Metals

1972 ◽  
Vol 50 (21) ◽  
pp. 2712-2714 ◽  
Author(s):  
B. S. Semwal ◽  
P. K. Sharma
Keyword(s):  
Shear Modulus ◽  
Numerical Integration ◽  
Elastic Constants ◽  
Characteristic Temperature ◽  
Debye Characteristic Temperature ◽  
Cubic Metals ◽  
Characteristic Temperatures ◽  
Metallic Element ◽  
Elastic Data ◽  
Direct Numerical Integration

The validity of Hill's formulas for the shear modulus of a polycrystalline cubic solid is examined by calculating the Debye characteristic temperature at 0 °K for a number of cubic metals using the measured elastic constants. The results are compared with calorimetric values and the numbers deduced from direct numerical integration of elastic data. Various methods give nearly similar results if the anisotropy of the metallic element is not excessively large.

Influence of lattice structure on motion of positrons and electrons through single crystals

1968 ◽  
Vol 46 (6) ◽  
pp. 543-550 ◽  
Author(s):  
E. Uggerhøj ◽  
J. U. Andersen
Keyword(s):  
Single Crystal ◽  
Single Crystals ◽  
Multiple Scattering ◽  
Lattice Structure ◽  
Energetic Electrons ◽  
Axis Direction ◽  
Lattice Position ◽  
Electrons And Positrons ◽  
Incoming Beam ◽  
Emission Yield

The emission yield from single crystals doped with β emitters is investigated. In the axis direction, energetic electrons emitted from a lattice position show a peak in yield up to 2.4 times the normal yield, whereas positrons emitted from the same positions show a dip by a factor of 4 from the normal yield. Electrons emitted from interstitial positions show no peak in yield. Energetic electrons transmitted through a thin single crystal experience increased multiple scattering when the incoming beam is aligned with an axis direction. The influence of atomic planes on the motion of electrons and positrons is also investigated. Furthermore, the electron peak and positron dip have been used for the localization of foreign atoms in single crystals.

Elastic Properties of L10-Ordered Single Crystals

2007 ◽  
Vol 26-28 ◽  
pp. 221-224 ◽  
Author(s):  
C. Wang ◽  
Katsushi Tanaka ◽  
Kyosuke Kishida ◽  
Haruyuki Inui
Keyword(s):  
Single Crystal ◽  
Temperature Dependence ◽  
Single Crystals ◽  
Elastic Properties ◽  
Elastic Constants ◽  
Elastic Anisotropy ◽  
Axial Ratio ◽  
Spectroscopy Technique ◽  
Complete Set

The temperature dependence of single-crystal elastic constants of L10-ordered single-crystals of FePd . A complete set of elastic constants has been determined with the resonance ultrasound spectroscopy technique. The compounds clearly show a tetragonal elastic anisotropy, c11 < c33 and c44 < c66. The temperature dependencies of the anisotropies are not simply explained by the variation of axial ratio (c/a) of the crystal.

Physical and Mechanical Properties of Single Crystals of Co-Al-W Based Alloys with L12 Single-Phase and L12/fcc Two-Phase Microstructures

2008 ◽  
Vol 1128 ◽  
Author(s):  
Haruyuki Inui ◽  
Katsushi Tanaka ◽  
Kyosuke Kishida ◽  
Norihiko L. Okamoto ◽  
Takashi Oohashi
Keyword(s):  
Mechanical Properties ◽  
Single Crystal ◽  
Single Crystals ◽  
Yield Stress ◽  
Liquid Helium ◽  
Elastic Constants ◽  
Single Phase ◽  
Physical And Mechanical Properties ◽  
Helium Temperature ◽  
Two Phase

AbstractSingle-crystal elastic constants of Co3(Al,W) with the cubic L12 structure have been experimentally measured by resonance ultrasound spectroscopy at liquid helium temperature. The values of all the three independent single-crystal elastic constants and polycrystalline elastic constants of Co3(Al,W) experimentally determined are 15~25% larger than those of Ni3(Al,Ta) but are considerably smaller than those previously reported. Two-phase microstructures with cuboidal L12 precipitates being well aligned parallel to <100> and well faceted parallel to {100} are expected to form very easily in Co-base superalloys because of the large value of E111/E100 and cij of Co3(Al,W). This is indeed confirmed by experiment. Values of yield stress obtained for both [001] and [¯123] orientations of L12/fcc two-phase single crystals moderately decrease with the increase in temperature up to 800°C and then decrease rapidly with temperature above 800°C without any anomaly in yield stress. Slip on {111} is observed to occur for both orientations in the whole temperature range investigated.

Relaxor Single-Crystal Plates with Nano-Size Ferroelectric Domains Applying to Ultrasonic Prove for Medical Uses

2016 ◽  
Vol 102 ◽  
pp. 57-64
Author(s):  
Toshio Ogawa ◽  
Taiki Ikegaya
Keyword(s):  
Bulk Modulus ◽  
Single Crystal ◽  
Grain Boundaries ◽  
Single Crystals ◽  
Young’S Modulus ◽  
Elastic Constants ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Poisson's Ratio ◽  
Domain Alignment

Sound velocities were measured in relaxor single-crystal plates, included in piezoelectric transducers for medical uses, using an ultrasonic precision thickness gauge with high-frequency pulse generation. The velocities were compared with the ones of piezoelectric ceramics in order to clarify characteristics of the single crystals. Estimating the difference in the sound velocities and elastic constants in the single crystals and ceramics, it was possible to evaluate effects of domain and grain boundaries on elastic constants. Existence of domain boundaries in single crystal affected the decrease in Young’s modulus, rigidity, Poisson’s ratio and bulk modulus. While existence of grain boundaries affected the decrease in Young’s modulus and rigidity, Poisson’s ratio and bulk modulus increased. It was thought these phinomina come from domain alignment by DC poling, and both the boundaries act as to absorb mechanical stress by defects due to the boundaries. In addition, the origin of piezoelectricity in single crystals is caused by low bulk modulus and Poisson’s ratio, and high Young’s modulus and rigidity in comparison with ceramics. On the contrary, the origin of piezoelectricity in ceramics is caused by high Poisson’s ratio by high bulk modulus, and furthermore, low Young’s modulus and rigidity due to domain alignment.

scholarly journals The behaviour of a single crystal of antimony subjected to alternating torsional stresses

1930 ◽  
Vol 127 (805) ◽  
pp. 431-453 ◽  
Keyword(s):  
Single Crystal ◽  
Single Crystals ◽  
Lattice Structure ◽  
Present Report ◽  
Maximum Density ◽  
Lattice Points ◽  
The Body ◽  
Atomic Density ◽  
Trigonal Symmetry ◽  
Two Factors

Previous experiments on the failure by fatigue of single crystals of aluminium, iron and zinc, representing the face-centred cubic, the body-centred cubic, and the close-packed hexagonal lattices, respectively, have shown that failure of metallic single crystals tends to occur by slip on the plane of greatest atomic density in the direction of greatest (linear) atomic density. The results obtained with iron seemed to indicate that of the two factors, the linear density is the more important. In all three lattices, however, the line of greatest density lay in the plane of greatest density, so that slip in the direction of the line of greatest density could always occur on the plane of greatest density and definite differentiation between the two factors was not possible. The structure of antimony (and also of bismuth), however, is such that the planes of maximum density do not contain any of the lines of maximum density, so that if the type of the slip plane were determined, definite evidence of the relative impor­tance of the two factors would be obtained. The present experiment was designed to yield this evidence; but in so far as the results are inconclusive, it is hoped to obtain further evidence by a similar experiment on a single crystal of bismuth. Lattice Structure .—The lattice structure of antimony as determined by A. Ogg (‘Phil. Mag.,’ vol. 42, p. 163 (1921)) and by James and Tunstall (‘Phil. Mag.,’ vol. 40, p. 233 (1920)) is a lattice of trigonal symmetry composed of two similar face-centred rhombohedral lattices, similarly orientated, displaced relative to each other along the longest diagonal of the rhombohedron (the axis of trigonal symmetry). The angle between any pair of edges of the rhombo­hedron is 86° 58' and the atoms are spaced along these edges at points 6·18 Å. apart. The ratio of the lengths into which the lattice points of either con­stituent lattice divide the long diagonals of the other lattice is given as 0·412 : 0·588 by Ogg and as 0·389 : 0·611 by James and Tunstall. For the purpose of the present report, the exact value of this ratio is of little importance; but where some value has to be inserted ( e. g ., in fig. 1) the value 0·4 : 0·6 has for convenience been assumed.

Physical and Mechanical Properties of Single Crystals of Co-Al-W Based Alloys with L12 Single-Phase and L12/fcc Two-Phase Microstructures

2010 ◽  
Vol 638-642 ◽  
pp. 1342-1347 ◽  
Author(s):  
Haruyuki Inui ◽  
Takashi Oohashi ◽  
Norihiko L. Okamoto ◽  
Kyosuke Kishida ◽  
Katsushi Tanaka
Keyword(s):  
Mechanical Properties ◽  
Single Crystal ◽  
Single Crystals ◽  
Yield Stress ◽  
Liquid Helium ◽  
Elastic Constants ◽  
Single Phase ◽  
Physical And Mechanical Properties ◽  
Helium Temperature ◽  
Two Phase

The values of all the three independent single-crystal elastic constants and polycrystalline elastic constants of Co3(Al,W) experimentally determined by resonance ultrasound spectroscopy at liquid helium temperature are 15~25% larger than those of Ni3(Al,Ta) but are considerably smaller than those previously calculated. Because of the large value of E111/E100 and cij of Co3(Al,W), two-phase microstructures with cuboidal L12 precipitates well aligned parallel to <100> and well faceted parallel to {100} are expected to form very easily in Co-base alloys, as confirmed indeed by experiment. Values of yield stress obtained for [001]-oriented L12/fcc two-phase single crystals moderately decrease with the increase in temperature up to 800°C and then decrease rapidly with temperature above 800°C without any anomaly in yield stress.

Mechanical Properties of Cr5Si3 with the D8m Structure

2011 ◽  
Vol 1295 ◽  
Author(s):  
Yuji Ochiai ◽  
Kyosuke Kishida ◽  
Katsushi Tanaka ◽  
Haruyuki Inui
Keyword(s):  
Crystal Structure ◽  
Mechanical Properties ◽  
Plastic Deformation ◽  
Thermal Expansion ◽  
Bulk Modulus ◽  
Single Crystal ◽  
Single Crystals ◽  
Elastic Constants ◽  
Deformation Behavior ◽  
Loading Axis

ABSTRACTElastic properties, thermal expansion and deformation behavior of Cr5Si3 with the D8m structure were investigated using single crystals. From the values of Cauchy pressures as well as the ratio of the polycrystalline bulk modulus (B) to shear moduls (G) estimated from single-crystal elastic constants (cij), deformation behavior of Cr5Si3 is expected to be relatively brittle compared to Mo5Si3 with the same crystal structure. However, plastic deformation of Cr5Si3 is confirmed above 900 ~ 1100 °C depending on the loading axis orientations.

The observation of defects on (100) CdTe surfaces by chemical etching

1992 ◽  
Vol 50 (2) ◽  
pp. 1424-1425
Author(s):  
M.E. Lee
Keyword(s):  
Single Crystal ◽  
Grain Boundaries ◽  
Single Crystals ◽  
Chemical Etching ◽  
Crystalline Perfection ◽  
Crystalline Defects ◽  
High Incidence ◽  
Crystallographic Defects ◽  
Cdznte Substrates ◽  
Device Technology

The crystalline perfection of bulk CdTe substrates plays an important role in their use in infrared device technology. The application of chemical etchants to determine crystal polarity or the density and distribution of crystallographic defects in (100) CdTe is not well understood. The lack of data on (100) CdTe surfaces is a result of the apparent difficulty in growing (100) CdTe single crystal substrates which is caused by a high incidence of twinning. Many etchants have been reported to predict polarity on one or both (111) CdTe planes but are considered to be unsuitable as defect etchants. An etchant reported recently has been considered to be a true defect etchant for CdTe, MCT and CdZnTe substrates. This etchant has been reported to reveal crystalline defects such as dislocations, grain boundaries and inclusions in (110) and (111) CdTe. In this study the effect of this new etchant on (100) CdTe surfaces is investigated.The single crystals used in this study were (100) CdTe as-cut slices (1mm thickness) from Bridgman-grown ingots.

Mounting an individual submicrometer sized single crystal

1996 ◽  
Vol 211 (6) ◽  
Author(s):  
R. B. Neder ◽  
M. Burghammer ◽  
Th. Grasl ◽  
H. Schulz
Keyword(s):  
Electron Microscope ◽  
Scanning Electron Microscope ◽  
Single Crystal ◽  
Single Crystals ◽  
High Vacuum ◽  
Nanometer Resolution ◽  
Micro Manipulator ◽  
Scanning Electron

AbstractWe developed a new micro manipulator for mounting individual sub-micrometer sized single crystals within a scanning electron microscope. The translations are realized via a commercially available piezomicroscope, adapted for high vacuum usage and realize nanometer resolution. With this novel instrument it is routinely possible to mount individual single crystals with sizes down to 0.1

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