>Frederic:
>
>See information at bottom of this message. My first response to your query
>seems to have bounced, I got a note from [email protected] that attachments are
>not typically forwarded, or HTML characters. So, I have copied the
>contents into the body of the email message, hoping this will work.
>Happy hunting/research! Perhaps sometime in the future there will be a
>simple and very "transparent" method for downloading every article ever
>published...but I need to request that you track these down yourself or
>with the help of colleagues nearby...hopefully you have the resources
>nearby to do that. Note that the strengths of diamond, silicon, germanium
>have been theoretically predicted from higher order elastic constants,
>see, e.g., paper(s) by A.L. Ruoff...perhaps also the hits I found on a
>simple search of "fracture strength of silicon" will be useful. I have
>not read them.
>
>Now, to have this MEMS forum be a *really useful* forum--once you have
>delved into this topic further, and and feel you can really thoroughly
>explain what is known about the fracture strength of silicon, you might
>(please) consider writing our a page or two on this topic, with
>references, and have this read and edited by a colleague whose English is
>flawless. Then, your contribution could be posted and archived in some
>useful way. After all, there are some issues that are fairly universal
>for MEMS/NEMS...stiffness and strength are examples, others are thermal
>expansion, etc.
>
>Sincerely, Rod Ruoff
>
>At 04:22 PM 2/8/01 +0100, Frederic Vanmeer wrote:
>>Hi everybody
>>
>>I have difficulty to found mechanical features of silicon.
>>In fact, I would to find the strength I must apply on a rectangular
>>piece of silicon to break it:
>>
>> | F (strength around 1.2 N)
>>* |
>>* V
>>************************* <- silicon piece h=250um, l=5mm, L=25mm
>>*
>>*<--------L------------>
>>
>>
>>If someone has ever worked on it, please help me
>>
"second order elastic constant silicon".
Bibliographic Information
Bibliographic Information
Third-order elastic constants of pure and doped germanium and silicon and
of indium antimonide and gallium arsenide from Keating's
theory. Bhatti, Surjit Singh; Singh, Devinder Pal. Dep. Phys., Guru
Nanak Dev
Univ., Amritsar, India. Acustica (1983), 53(5), 262-3. CODEN:
ACUSAY ISSN: 0001-7884. Journal written in English. CAN
100:28257 AN 1984:28257 CAPLUS (Copyright 2001 ACS)
Abstract
The 3rd-order elastic consts. of pure and doped Ge, Si, InSb, and GaAs are
explained on the basis of Keatings theory.
Bibliographic Information
Measurement of a third-order elastic constant in silicon by a comparison
method. Duquesne, J. -Y. L.M.D.H., Universite Pierre et Marie
Curie/CNRS (UMR 7603), Paris, Fr. J. Acoust. Soc. Am. (2000), 108(3,
Pt. 1), 946-948. CODEN: JASMAN ISSN: 0001-4966. Journal written in
English. CAN 133:313972 AN 2000:708656 CAPLUS (Copyright 2001 ACS)
Abstract
The third-order elastic const. C111 of silicon is measured with a
comparison method, based on the interaction between longitudinal acoustic
waves. The value is in good agreement with published values and
demonstrates the validity of the method.
Bibliographic Information
New estimates of the third-order elastic constants for isotropic aggregates
of cubic crystals. Lubarda, V. A. Dep. Mechanical Aerospace
Engineering, Arizona State Univ., Tempe, AZ, USA. J. Mech. Phys.
Solids (1997), 45(4), 471-490. CODEN: JMPSA8 ISSN:
0022-5096. Journal written in English. CAN 126:310558 AN
1997:280264 CAPLUS (Copyright 2001 ACS)
Abstract
An improved method, based on an extension of the self-consistent method
from the linear theory, is proposed to evaluate the effective 3rd-order
elastic consts. for isotropic aggregates of cubic crystals. The calcd.
consts. are compared with the Voigt and Reuss-Type ests., which are
currently the only other anal. ests. available for these consts. The
agreement between calcns. and exptl. data is then discussed.
Bibliographic Information
Acoustoelastic measurement of second- and third-order elastic constants in
silicon carbide and alumina particulate-reinforced aluminum metal matrix
composites. Saigal, A.; Krikorian, S.; Leisk, G. G. Department of
Mechanical Engineering, Tufts University, Medford, MA, USA. Rev.
Prog. Quant. Nondestr. Eval. (1996), 15B 1637-1644. CODEN:
RPQEDF Journal written in English. CAN 125:174416 AN
1996:523151 CAPLUS (Copyright 2001 ACS)
Abstract
Acoustoelastic testing of Al2O3/Al 6061 and SiC/Al-Si composites was
preformed. The 2nd-order elastic consts., specifically modulus of
elasticity and Lame consts., of both composite systems vary linearly with
the amt. of reinforcement.
Bibliographic Information
Third-order elastic constants of pure and doped germanium and silicon and
of indium antimonide and gallium arsenide from Keating's
theory. Bhatti, Surjit Singh; Singh, Devinder Pal. Dep. Phys., Guru
Nanak Dev
Univ., Amritsar, India. Acustica (1983), 53(5), 262-3. CODEN:
ACUSAY ISSN: 0001-7884. Journal written in English. CAN
100:28257 AN 1984:28257 CAPLUS (Copyright 2001 ACS)
Abstract
The 3rd-order elastic consts. of pure and doped Ge, Si, InSb, and GaAs are
explained on the basis of Keatings theory.
Bibliographic Information
Third-order elastic constants and Grueneisen parameters of silicon and
germanium between 3 and 300°K. Philip, Jacob; Breazeale, M. A. Dep.
Phys., Univ. Tennessee, Knoxville, TN, USA. J. Appl.
Phys. (1983), 54(2), 752-7. CODEN: JAPIAU ISSN:
0021-8979. Journal written in English. CAN 98:99082 AN
1983:99082 CAPLUS (Copyright 2001 ACS)
Abstract
A method is given to det. all 6 independent 3rd-order elastic (TOE) consts.
of diamond-like solids as functions of temp. from measured values of the
ultrasonic nonlinearity parameters. Ultrasonic harmonic generation expts.
along the 3 principal directions of a cubic crystal lead to the detn. of
the nonlinearity parameters, which contain 3 linear combinations of TOE
consts. These data are sufficient to det. the 3 anharmonic 1st and 2nd
neighbor force consts. in the Keating model for diamond-like solids. The
Keating model force const. and all 6 2nd-order elastic consts. at 3-300 K
were evaluated for Si and Ge. Most of the TOE consts. of Si and Ge are
smoothly varying functions of temp.; however, C123 and C144 go through 0
and assume pos. values at low temps. To det. whether the behavior of the
calcd. TOE consts. is reasonable, they were used to calc. the generalized
Grueneisen parameters, g, in the quasiharmonic approxn. and plotted g as a
function of temp. These curves agree with curves obtained from thermal
expansion expts. The pressure-dependence of the 2nd-order elastic consts.
and the Anderson Grueneisen parameters over the same temp. range.
Bibliographic Information
Relation of the third-order elastic constants to other nonlinear
quantities. Breazeale, M. A.; Philip, Jacob. Dep. Phys., Univ.
Tennessee, Knoxville, TN, USA. Ultrason. Symp.
Proc. (1981), 1 425-31. CODEN: ULSPDT ISSN:
0090-5607. Journal written in English. CAN 97:31591 AN
1982:431591 CAPLUS (Copyright 2001 ACS)
Abstract
Seeking an "ideal" solid is a reasonable way to begin to understand the
behavior of the TOE (3rd-order elastic) consts. The simplest model for the
"ideal" solid probably is a central forces, nearest-neighbor model. The
central forces, nearest-neighbor model seems adequate nominally to describe
Cu, at least at 2 temps., but it must be improved by considering noncentral
forces of next-nearest neighbors to describe Si. In this case the improved
model enables one to evaluate all 6 TOE consts. of Si from the measurements
of 3 combinations of TOE consts. and to plot all 6 from 3 to 300 K. A test
of the results is made by calcg. the Grueneisen g for Si from the calcd.
TOE consts. The use of the Keating model leads to values of the TOE
consts. which are more preferable to those obtained by combining the
results with measurements of the pressure dependence of ultrasonic wave
velocity in Si.
Bibliographic Information
Temperature variation of some combinations of third-order elastic constants
of silicon between 300 and 3°K. Philip, Jacob; Breazeale, M. A. Dep.
Phys., Univ. Tennessee, Knoxville, TN, USA. J. Appl.
Phys. (1981), 52(5), 3383-7. CODEN: JAPIAU ISSN:
0021-8979. Journal written in English. CAN 95:71365 AN
1981:471365 CAPLUS (Copyright 2001 ACS)
Abstract
The nonlinearity parameters of Si were detd. by ultrasonic harmonic
generation between room temp. and 3 K. The temp. dependence of 3 linear
combinations of 3rd-order elastic (TOE) consts. of Si was studied. Between
room temp. and 77 K, the magnitude of the TOE consts. does not vary much as
a function of temp. Between 77 and 3 K, C111 changes by 3.5%, C112 + 4C166
changes by 11.7%, and C123 + 6C144 + 8C456 changes by -207%. All these
combinations are neg. at room temp. as well as at low temps. except C123 +
6C144 + 8C456 which is pos. below 8 K. Room-temp. values of the strain
generalized Grueneisen parameters of Si we calcd. from measured
nonlinearity parameters and compared with existing values. Complete sets
of 3rd-order elastic consts. at 298, 77, and 4 K were calcd. by combining
the nonlinearity parameters with pressure derivs. of elastic consts.
measured by Beattie and Schirber (1970).
Bibliographic Information
Lattice theory of third order elastic constants of germanium and
silicon. Srinivasan, Ramaswami. Pennsylvania State Niv., University
Park, PA, USA. J. Phys. Chem.
Solids (1967), 28(12), 2385-96. CODEN: JPCSAW Journal written in
English. CAN 68:63417 AN 1968:63417 CAPLUS (Copyright 2001 ACS)
Abstract
The lattice theory of 3rd order elastic consts. is applied to Ge and
Si. For general interactions up to 2nd neighbors, the 2nd and 3rd order
coupling parameters are derived for the Ge lattice. There are 26
independent parameters which reduce to 3 when only the 1st-neighbor
interaction is considered. In the latter case, 4 simple identities are
obtained among the 2nd- and 3rd-order elastic consts. One of these
identities was 1st derived by Born. The left and right hand sides of the
identities are calcd. from the exptl. 2nd- and 3rd-order elastic consts.
reported in the literature for Ge and Si. The Born identity is well
satisfied in Ge and Si indicating that the 2nd-order elastic consts. of Ge
and Si can be well accounted for by a 1st-neighbor interaction
model. However, the other 3 identities are not well satisfied. This
indicates that for the 3rd order elastic consts. the interactions beyond
1st neighbors play a decisive part.
Bibliographic Information
Fourth order elastic moduli of diamond structure materials. Gerlich,
D. School Physics Astronomy, Tel Aviv University, Tel
Aviv, Israel. J. Appl. Phys. (1995), 77(9), 4373-9. CODEN:
JAPIAU ISSN: 0021-8979. Journal written in English. CAN
122:274650 AN 1995:524574 CAPLUS (Copyright 2001 ACS)
Abstract
The values of the fourth order elastic moduli (FOEM) for the diamond
structure elements, silicon and germanium, have been calcd. The derivation
utilizes the Keating model, assuming that both the third and fourth order
terms in the interaction potential are composed of a bond-stretch, an
angle-bend, and a mixed bond-stretch angle-bend term. The three force
consts. in the fourth order interaction potential are evaluated from the
measurements of the sound velocity under pressure, hence, numerical values
for all 11 FOEM may be obtained. The set of FOEM thus calcd. shows
markedly different characteristics than the analogous quantities for other
materials, e.g., the alkali halides.
Bibliographic Information
Anharmonic elastic and phonon properties of silicon. Vanderbilt, David;
Taole, S. H.; Narasimhan, Shobhana. Dep. Phys., Harvard
Univ., Cambridge, MA, USA. Phys. Rev. B: Condens.
Matter (1989), 40(8), 5657-68. CODEN: PRBMDO ISSN:
0163-1829. Journal written in English. CAN 111:222440 AN
1989:622440 CAPLUS (Copyright 2001 ACS)
Abstract
A unified framework is suggested for the discussion of anharmonic phonon
coupling consts. and anharmonic elastic consts. in diamond-structure
materials. A summary is given, within this framework, of those anharmonic
consts. which have previously been detd. exptl. or theor. for Si. New
local-d. total-energy calcns. for X-point phonons in Si were used to add to
this database of known anharmonic consts. It is proposed that empirical
models for interat. potentials should be constrained to fit this
database. A generalized Keating model which has been fitted in this way,
with 2- and 3-body couplings of 3rd and 4th order, is presented. It can be
used to calc. arbitrary anharmonic photon couplings through 4th order.
Bibliographic Information
Thermal expansion and elastic anisotropies of silicon carbide as related to
polytype structure. Li, Z.; Bradt, R. C. Dep. Mater. Sci.
Eng., Univ. Washington, Seattle, WA, USA. Ceram.
Trans. (1989), 2(Silicon Carbide '87), 313-39. CODEN:
CETREW Journal written in English. CAN 111:139285 AN
1989:539285 CAPLUS (Copyright 2001 ACS)
Abstract
The structural relations between the polytypes of SiC are such that the
anisotropic thermal expansion coeffs. (2nd-order tensors) and
single-crystal elastic consts. (4th-order tensors) can be systematically
related to the structural stacking layer sequence. The concept of the
fraction of hexagonal stacking is generally applied to describe the
anisotropic thermal expansion coeffs. The single-crystal elastic
anisotropy for the SiC polytype structures and the temp. dependencies of
the anisotropies are discussed. Pertinent to transient thermal stresses
and to processing-related internal micromech. residual stresses, the
concept of an anisotropic thermoelastic stress index is presented. Its
anisotropy is graphically illustrated for the 3C and 6H SiC polytypes. In
addn. to its general thermoelastic stress utility, it is useful for
predicting the most desirable crystal (whisker) growth orientations for SiC
whisker incorporation into composite matrixes.
Bibliographic Information
Temperature dependence of the elastic constants for solids of cubic
symmetry. Application to germanium and silicon. Toupance, N. Cent.
Sci. Polytech., Univ. Paris-Nord, Villetaneuse, Fr. Phys. Status
Solidi B (1987), 140(2), 361-8. CODEN: PSSBBD ISSN:
0370-1972. Journal written in English. CAN 107:106693 AN
1987:506693 CAPLUS (Copyright 2001 ACS)
Abstract
The extension of the finite strain expansion of the Mie-Grueneisen equation
(taking into account the elastic consts. in the ref. configuration up to
the 4th order) was used to derive the temp. dependence of the volumetric
compression and of the 2nd-order elastic adiabatic moduli of cubic
solids. Numerical results are given for Ge and Si and compared to exptl.
data. Finally, the 2nd pressure deriv. of these consts. was estd. at zero
pressure and 300 K.
Bibliographic Information
First-principles calculation of stress. Nielsen, O. H.; Martin, Richard
M. Xerox Palo Alto Res. Cent., Palo Alto, CA, USA. Phys. Rev.
Lett. (1983), 50(9), 697-700. CODEN: PRLTAO ISSN:
0031-9007. Journal written in English. CAN 98:117357 AN
1983:117357 CAPLUS (Copyright 2001 ACS)
Abstract
A generalization of the virial theorem is presented for all components of
the av. stress tensor of arbitrary systems of interacting
particles. Explicit expressions are given for local-d.-functional calcns.
and the method is tested by ab initio pseudopotential calcns. on
Si. Accurate detns. are made of lattice const., bulk moduli, 2nd-, 3rd-,
and 4th-order elastic consts., and the internal strain parameter z. The
calcd. and exptl. values agreed except for z.
Bibliographic Information
Fourth-order elastic constant, C1111, of cubic crystals. Prasad, O. H.;
Suryanarayana, M. Coll. Sci., Osmania
Univ., Hyderabad, India. Phys. Status Solidi
B (1982), 112(2), 627-31. CODEN: PSSBBD ISSN:
0370-1972. Journal written in English. CAN 97:136851 AN
1982:536851 CAPLUS (Copyright 2001 ACS)
Abstract
A method for the evaluation of C1111, the 4th-order elastic const. of the
octahedral class of cubic crystals is being suggested which does not
involve measurements on crystals using uniaxial stress. Values of C1111 of
26 cubic crystals were evaluated at room temp. and also at some lower
temps. in cubic NaCl, KCl, RbCl, RbBr, RbI, Ge, and Si.
Bibliographic Information
Anharmonic contribution to mode softening in vanadium-silicon
(V3Si). Achar, B. N. N.; Barsch, G. R. Dep. Phys., Pennsylvania
State Univ., University Park, PA, USA. Phys. Rev. B: Condens.
Matter (1979), 19(7), 3761-75. CODEN: PRBMDO ISSN:
0163-1829. Journal written in English. CAN 91:47609 AN
1979:447609 CAPLUS (Copyright 2001 ACS)
Abstract
In order to assess the magnitude and significance of anharmonic effects in
V3Si, the Landau theory of R. Bhatt and W. McMillan (1978) for the
coupled-mode charge-d. wave instability was extended to higher order. The
higher-order coupling parameters were detd. empirically and used to calc. 9
second-through fourth-order elastic consts. as a function of temp. The
nonlinear stress-strain curve calcd. from these results agrees with exptl.
data. The elastic-shear-mode softening was investigated in the
quasiharmonic anisotropic-elastic-continuum approxn., in which anharmonic
effects enter through the third- and fourth-order elastic consts. A strong
enhancement of the electronically driven instability by the anharmonic
phonon-phonon interaction was found.
Bibliographic Information
Higher order elastic constants and nonlinear stress-strain relation for
vanadium-silicon (V3Si). Barsch, G. R. Mater. Res.
Lab., Pennsylvania State Univ., University Park, Pa., USA. Solid
State Commun. (1974), 14(10), 983-7. CODEN: SSCOA4 Journal written in
English. CAN 81:55257 AN 1974:455257 CAPLUS (Copyright 2001 ACS)
Abstract
Relations for the 3rd- and 4th-order elastic consts. are derived from a
Landau-Devonshire-type free energy function for A15-type crystals which
undergo the structural transformation at low temps. Application to
transforming V3Si at 2°K gives unusually large numerical values for the
consts. The calcd. stress-strain relation is in semiquant. agreement with
the strongly nonlinear behavior measured directly.
Bibliographic Information
Anharmonic interactions in diamond-type crystals. Jex, H. Inst.
Theor. Phys., Univ. Frankfurt/Main, Frankfurt/Main, Ger. Phys. Status
Solidi B (1971), 45(1), 343-55. CODEN: PSSBBD Journal written in
English. CAN 75:41557 AN 1971:441557 CAPLUS (Copyright 2001 ACS)
Abstract
The potential energy of diamond, Si, and Ge crystals has been expanded in a
double power series of the infinitesimal strain parameters and phonon
coordinates. Third and 4th order expansion coeffs. have been fitted to
give reasonable agreement with the Grueneisen parameters of the individual
modes of vibration, the mean Grueneisen parameters and thermal expansion
coeffs., the 3rd order elastic consts., and the temp. dependence of the
elastic consts. Calcns. have been made for the mass operators of normal
modes propagating in the [100] and [111] directions. The relative
renormalization of the low energy TA (transverse acoustic) modes in Ge and
Si is of the order of 10%, whereas it is one order of magnitude less for
phonons of the other branches.
Bibliographic Information
Stress dependence of ultrasonic velocity and dislocation kink motion in
silicon. Suzuki, Tetsuro; Chick, Bruce B.; Elbaum, Charles. Brown
Univ., Providence, R. I., USA. Appl. Phys.
Lett. (1965), 7(1), 2-4. CODEN: APPLAB Journal written in
English. CAN 66:109077 AN 1967:109077 CAPLUS (Copyright 2001 ACS)
Abstract
The change in velocity of 50-Mc. shear waves in single-crystal Si was
measured at 25° as a function of uniaxial stress. A Si crystal was grown
by the float zone technique in the [111] direction having a dislocation d.
of 500/cm.2 and p-type resistivity of 200 ohm-cm. Deviations from
linearity for bias stresses <108 dynes/cm.2 were observed. A mobile
kink-model of dislocations is proposed as the cause of the deviation, and
expts. indicate that dislocations are mobile in Si at room temp. with no
large generation of new kinks. The stress dependence of the velocity is
linear for stresses >7 ´ 107 dynes/cm.2, which indicates that the deviation
from linearity found at lower stresses is not due to a 4th-order elastic
const. in the crystal structure.
Bibliographic Information
Effect of strain on phonons in Si, Ge, and Si/Ge heterostructures. Sui,
Zhifeng; Herman, Irving P. Dep. Appl. Phys., Columbia Univ., New
York, NY, USA. Phys. Rev. B: Condens.
Matter (1993), 48(24), 17938-53. CODEN: PRBMDO ISSN:
0163-1829. Journal written in English. CAN 120:149425 AN
1994:149425 CAPLUS (Copyright 2001 ACS)
Abstract
The dispersion relations for optical and acoustic phonons in bulk Si and
Ge, in Si and Ge strained layers grown on (001) and (111) surfaces, and in
ultrathin Si/Ge superlattices at ambient pressure and under hydrostatic
pressure were studies theor. by using a modified Keating model. This model
included four interactions, which involved up to the fifth-nearest-neighbor
atoms, and force consts. that depended on strain. These strain-modified
force consts. are related to specific cubic anharmonic terms in the
potential energy, and also to the empirical parameters p, q, and r that
have been used to describe zone-center phonon shifts and splittings arising
from strain. This model was used to obtain the mode Grueneisen parameters
gi throughout the Brillouin zone for bulk c-Si and c-Ge, and explicit
analytic expressions for gi at the zone center and boundaries. Biaxial
strain in the (001) plane was shown to affect phonon dispersion very
differently than in previous work that used a much simpler model. For Si
and Ge grown on a (111) substrate, the frequency shift due to the biaxial
strain for the TO-phonon mode was found to be almost independent the of
wave vector. The pressure-induced change in the frequency of confined LO
phonons in a Si12Ge4 superlattice predicted by the model agreed with the
change measured previously by Raman scattering. This modified Keating
model was also used to obtain the second- and third-order elastic consts.
for Si and Ge.
Bibliographic Information
Reinvestigation of the TA modes in germanium and silicon in Born-von Karman
model. Jian, Wang; Kaiming, Zhang; Xide, Xie. Dep. Phys., Fudan
Univ., Shanghai, Peop. Rep. China. Solid State
Commun. (1993), 86(11), 731-4. CODEN: SSCOA4 ISSN:
0038-1098. Journal written in English. CAN 119:127105 AN
1993:527105 CAPLUS (Copyright 2001 ACS)
Abstract
The authors give the correct dynamic matrix elements for the diamond
structure up to the sixth neighbors in Born-von Karman model. The
importance of the fifth neighbor to the characteristic flattening of the
transverse-acoustic (TA) modes in Ge and Si is confirmed by extensive Monte
Carlo iterative search of the parameter space. This indicates that range
up to at least fifth neighbor should be considered when constructing
potential models for Ge and Si in order to properly produce the lattice
dynamics.
Research Topic task started on Sun Feb 11, 2001 at 4:03 PM
Bibliographic Information
On the ultimate yield strength of diamond: finite elasticity
approach. Luo, Huan; Ruoff, Arthur L.. Dep. Materials Sci.
Eng., Cornell Univ., Ithaca, NY, USA. AIP Conf.
Proc. (1994), 309(High-Pressure Science and Technology--1993, Pt.
1), 511-14. CODEN: APCPCS ISSN: 0094-243X. Journal written in
English. CAN 122:269355 AN 1995:464610 CAPLUS (Copyright 2001 ACS)
Abstract
A method based on finite elasticity theory, to compute the ultimate
strength of solids in the absence of defect motion has been proposed by
A.L. Ruoff (1978) and used to compute the yield strength of diamond under
uniaxial stress conditions. This method utilizes only the measured second-
and third-order elastic consts. In the present paper, we extend the anal.
of diamond to the case of uniaxial strain along the three selected
directions of the cubic system, [100], [110] and [111]. This case is
considered because it represents a good approxn. to the state of strain at
the point of max. shear stress (which is the cause of yielding) in a loaded
diamond anvil. The results are used as the basis for estg. the ultimate
compressive and tensile strengths of diamond.
Bibliographic Information
Megabar pressures in submicron volumes. Ruoff, A. L.. Cornell
Univ., Ithaca, NY, USA. Editor(s): Vodar, Boris; Marteau,
Philippe. High Pressure Sci. Technol., Proc. Int. AIRAPT Conf.,
7th (1980), Meeting Date 1979, 1 127-32. Publisher: Pergamon, Oxford,
Engl CODEN: 46ELAD Conference; General Review written in English. CAN
95:103463 AN 1981:503463 CAPLUS (Copyright 2001 ACS)
Abstract
The topics reviewed with 18 refs. include: the (diamond indentor
[DI])-(diamond anvil [DA]) technique for generating ultrahigh pressures
(.apprx.1.5 Mbar); theor. compressive strength of diamond; the Hertz theory
and the limits to the pressure obtainable with the DI-DA method; and
interdigitated microelectrodes for elec.-resistance measurements on very
small samples at ultrahigh pressures.
Bibliographic Information
On the yield strength of diamond. Ruoff, Arthur L.. Dep. Mater. Sci.
Eng., Cornell Univ., Ithaca, NY, USA. J. Appl.
Phys. (1979), 50(5), 3354-6. CODEN: JAPIAU ISSN:
0021-8979. Journal written in English. CAN 91:66589 AN
1979:466589 CAPLUS (Copyright 2001 ACS)
Abstract
The yield stress of strong single crystals was estd. from the Hugoniot
elastic limit and the 2- and 3-order elastic consts. Data on Ge and Si
were analyzed. The dynamic yield stresses obtained are compared with a
directly measured static value for Si and for values obtained from Knoop
hardness tests. The dynamic results for Si and Ge are used along with a
scaling law to est. the yield stress for diamonds. This, in turn, compares
favorably with the values deduced from Knoop hardness tests and a directly
measured static yield stress. The yield stress of diamond is .apprx.35 GPa.
Bibliographic Information
The compressive strength of perfect diamond. Nelson, David A., Jr.;
Ruoff, Arthur L.. Dep. Mater. Sci. Eng., Cornell
Univ., Ithaca, NY, USA. J. Appl.
Phys. (1979), 50(4), 2763-4. CODEN: JAPIAU ISSN:
0021-8979. Journal written in English. CAN 91:47617 AN
1979:447617 CAPLUS (Copyright 2001 ACS)
Abstract
Earlier work on the theor. compressive strength of perfect-diamond cubic
crystals under [100] loading is extended to the case of [111] loading. The
latter are much stronger. The compressive strength of perfect diamond
loaded in the [111] direction is 4.1 Mbars.
Bibliographic Information
On the ultimate yield strength of solids. Ruoff, Arthur L.. Dep.
Mater. Sci. Eng., Cornell Univ., Ithaca, N. Y., USA. J. Appl.
Phys. (1978), 49(1), 197-200. CODEN: JAPIAU ISSN:
0021-8979. Journal written in English. CAN 88:113621 AN
1978:113621 CAPLUS (Copyright 2001 ACS)
Abstract
A method is presented for obtaining the ultimate strength of solids in the
absence of defect motion. The procedure which involves finite elasticity
theory and measured higher-order elastic coeffs. is utilized to compute the
ultimate tensile and compressive yield stress of Ge and Si crystals loaded
in the [100] direction. These results are used as the basis for estg. the
ultimate compressive strength of diamond.
Bibliographic Information
The influence of backgrinding on the fracture strength of 100 mm diameter
(111)p-type silicon wafers. Mcguire, K.; Danyluk, S.; Baker, T. L.;
Rupnow, J. W.; Mclaughlin, D. Department of Civil Engineering, Mechanics
and Metallurgy, University of Illinois at
Chicago, Chicago, IL, USA. J. Mater.
Sci. (1997), 32(4), 1017-1024. CODEN: JMTSAS ISSN:
0022-2461. Journal written in English. CAN 126:218867 AN
1997:143441 CAPLUS (Copyright 2001 ACS)
Abstract
The influence of grinding geometry and damage depth on the fracture
strength of 100 mm diam. (111) p-type Si wafers was studied. The fracture
strengths were measured in a biaxial flexure test after the wafers were
ground to 0.36 mm from 0.53 mm thick, in a grinding app. that produces a
swath of swirls on the Si wafers surfaces. Anal. of orientations of the
swirl geometries and fracture probability was used to deduce the fracture
strength relative to the crystallog. orientation of the wafers. Optical
and SEM of beveled, and cleaved and etched samples was used to measure the
damage depths from selected locations on the wafers. The depth of damage
and fracture strengths were correlated to the geometry of the backgrind
swirl pattern and the relative position of the orientation flat. The
damage depth was smaller when the swirl path was parallel or at 45° to the
orientation flat as compared to the swirl paths at 90 and 135°
orientations. As a result, the wafers ground in the former orientations
had a higher fracture strength than those of the latter orientations (136
and 124 MPa vs. 100 and 103 MPa, for the four orientations, resp.).
Bibliographic Information
Fracture strength of silicon nitride under biaxial stresses. Kokaji,
Akira; Uchimura, Hiroshi; Kaji, Masaki. Cent. Res. Lab., KYOCERA Co.,
Ltd., Kokubu, Japan. J. Ceram. Soc.
Jpn. (1992), 100(Nov.), 1304-8. CODEN: JCSJEW Journal written in
Japanese. CAN 118:130302 AN 1993:130302 CAPLUS (Copyright 2001
ACS)
Abstract
The fracture strength of silicon nitride was studied under biaxial stress
states. Multiaxial fracture distribution functions by several fracture
criteria were employed to analyze tension/torsion, compression/torsion
tests. The most appropriate criterion was Shetty's empirical equation
(parameter c = 1.4) and the modified G criterion (parameter b = 0.9). The
fracture strength of a disk for a spin test was estd. by the equiv. normal
stress of Shetty's empirical equation and the modified G criterion. Good
agreement between the exptl. data and the estd. values were obtained.
Bibliographic Information
Crack healing and fracture strength of silicon crystals. Yasutake, K.;
Iwata, M.; Yoshii, K.; Umeno, M.; Kawabe, H. Fac. Eng., Osaka
Univ., Suita, Japan. J. Mater. Sci. (1986), 21(6), 2185-92. CODEN:
JMTSAS ISSN: 0022-2461. Journal written in English. CAN
105:70403 AN 1986:470403 CAPLUS (Copyright 2001 ACS)
Abstract
The influence of annealing at 700-1100° on fracture strength of pre-cracked
Si wafers was examd. by 4-point bending tests at room temp. The fracture
strengths of the specimens annealed in O increased significantly with
increasing annealing temp. Annealing in vacuum showed little influence on
the fracture strength. The strength increase by the annealing in O is
caused by crack healing. The crack surfaces are probably rebonded by the
formation of a thin oxide layer at the crack interface. The activation
energy for the crack healing is 2.0 eV, which is consistent with that of
the reaction-limited growth of a thin oxide film.
Bibliographic Information
Mechanics of strength-degrading contact flaws in silicon. Lawn, B. R.;
Marshall, D. B.; Chantikul, P. Sch. Phys., Univ. New South
Wales, Kensington, Australia. J. Mater.
Sci. (1981), 16(7), 1769-75. CODEN: JMTSAS ISSN:
0022-2461. Journal written in English. CAN 95:89276 AN
1981:489276 CAPLUS (Copyright 2001 ACS)
Abstract
The micromechanics of indentation-induced flaws in monocryst. Si were
studied in relation to strength detn. The evolution of the
deformation-fracture pattern during contact with a Vickers pyramid is
described. The response of the cracks in subsequent strength testing is
followed. A precursor stage of stable growth was obsd. prior to attaining
a failure configuration, consistent with augmentation of the applied
tensile (flexural) loading by the residual contact component. No
detectable slow crack growth due to environmental influence was found. The
relevance of brittleness to the mech. behavior of Si components as a
function of fabrication and prospective service conditions is discussed.
