How To Find Experimental Value

Experimental Value

Experimental values of stacking-fault energies (SFE) offer a method of providing energy differences between stable and metastable close-packed structures.

From: Pergamon Materials Series , 1998

Mass transfer

Charles H. Forsberg , in Heat Transfer Principles and Applications, 2021

eleven.3.1 Binary gas diffusion coefficient

Many experiments have been performed to determine binary diffusion coefficients. And, several correlation equations have been proposed to fit experimental data and to predict the coefficient for pairs of gases for which experimental data are unavailable [one–6]. One such equation, past Fuller, Schettler, and Giddings [5], was developed by correlating data for 340 experiments. The equation has a very proficient average error of only 4.3%. The equation is

(11.14) $D_{AB}=\frac{{\text{undefined}10}^{-7}{T}^{1.75}{\left(\frac{1}{G_A}+\frac{\mathrm{i}}{M_B}\right)}^{\mathrm{i}/2}}{P{\left[{\left(V_A\right)}^{1/\mathrm{three}}+{\left(V_B\right)}^{\mathrm{i}/\mathrm{three}}\right]}^2}$

where $D_{AB}$   =   binary gas diffusion coefficient (grandⁱⁱ/southward),

P   = total pressure level (atm),

T  =   temperature (K),

M  =   molecular weight of the gas (kg/kmol),

$V_A\text{ and}{V}_B$   =   diffusion molecular volumes of the ii gases.

The diffusion molecular volumes of some simple gases are given in Tabular array xi.ane. For organic vapors, the diffusion volume increments given in Table 11.2 may be accordingly summed to obtain an equivalent volume to use in Eq. (11.14). For instance, if methane (CH_four) is Gas A, and so, using the values in Tabular array xi.ii, $V_A=\left(16.5\right)+4\left(1.98\right)=24.42$ .

Table 11.i. Diffusion volumes of simple molecules.

H2	vii.07	Kr	22.8	(Xe) a	37.nine
He	two.88	CO	18.9	(SF6)	69.7
N2	17.ix	COii	26.9	(Cltwo)	37.7
Oii	16.6	N2O	35.nine	(Br2)	67.2
Air	20.1	NHiii	xiv.ix	(And then2)	41.i
Ne	v.59	H2O	12.vii
Ar	16.1

a

Items with parentheses are based on only a few data points and may be less accurate than the other items.

Table 11.ii. Atomic improvidence volume increments.

C	16.v	(N) a	five.69
H	1.98	(Cl)	nineteen.5
O	v.48	(S)	17.0

a

Items with parentheses are based on merely a few information points and may exist less accurate than the other items.

It is seen from Eq. (11.14) that the diffusion coefficient is directly proportional to the temperature to the 1.75 ability and inversely proportional to the force per unit area. Hence, if $D_{AB}$ is known at Country 1, then $D_{AB}$ at State 2 tin exist approximated by using the relation

(xi.fifteen) ${\left(D_{AB}\right)}_2={\left(D_{AB}\right)}_1\left(\frac{P_1}{P_{\mathrm{ii}}}\right){\left(\frac{T_2}{T_1}\right)}^{1.75}$

(Note: Temperatures in Eq. (11.15) must exist in absolute units, e.chiliad., Kelvin.)

Experimental values of gas diffusion coefficients are given in Tabular array xi.3. Most of the experimental values in the table are from a listing in Ref.[five], which can exist consulted for the original data sources. If the listed coefficient value was for a temperature and/or pressure different from 300   G and 1   atm, and so Eq. (11.fifteen) was used to modify the value to the 300   K, 1   atm reference values.

Tabular array 11.iii. Binary gas diffusion coefficients (at 300   K and one   atm).

Gases	DAB  × 10iv	Gases	DAB  × 104	Gases	DAB  × 104
	(thouii/s)		(mtwo/s)		(one thousand2/southward)
H2–air	0.73	Hii–Ntwo	0.81	N2–CO	0.22
He–air	0.71	H2–He	i.fourteen	N2–CO2	0.17
CO2–air	0.17	H2–Ar	0.89	Ntwo–NH3	0.26
Oii–air	0.21	Hii–CO	0.76	Ar–CO	0.nineteen
H2O–air	0.26	Htwo–CO2	0.66	Ar–CO2	0.15
NH3–air	0.25	Htwo–NH3	0.86	Ar–O2	0.21
So2–air	0.13	He–Ar	0.75	Ar–NHthree	0.24
H2–H2O	0.97	He–CO	0.72	Otwo–NHiii	0.26
He–HtwoO	0.88	He–CO2	0.61	Oii–N2	0.21
CO2–H2O	0.xix	He–Nii	0.74	CO–COii	0.16
N2–H2O	0.25	He–NH3	0.85	CO–NHiii	0.25
Oii–H2O	0.27	He–Oii	0.73	CO2–N2O	0.12

Example xi.two

Improvidence coefficient of oxygen in air

Problem

What is the binary diffusion coefficient of oxygen in air at 500   K and i.5   atm?

Solution

From Tabular array 11.3, the binary diffusion coefficient of oxygen in air at 300   Thousand and 1   atm is 0.21   ×   10⁻⁴  m²/s. Let Country ane be 300   K and 1   atm and State two be 500   G and one.5   atm. So, from Eq. (xi.15),

${\left(D_{AB}\right)}_2={\left(D_{AB}\right)}_1\left(\frac{P_1}{P_{\mathrm{ii}}}\right){\left(\frac{T_{\mathrm{ii}}}{T_{\mathrm{i}}}\right)}^{1.75}=0.21\times {10}^{-\mathrm{four}}\left(\frac{1}{\mathrm{one.v}}\right){\left(\frac{500}{300}\right)}^{1.75}=\mathrm{three}\mathrm{.4}\times \mathrm{1}{\mathrm{0}}^{-\mathrm{5}}{\mathrm{m}}^{\mathrm{2}}/\mathrm{southward}$

The binary diffusion coefficient of oxygen in air at 500   K and one.5   atm is $\mathbf{3}\mathbf{.4}\times \mathbf{1}{\mathbf{0}}^{\mathbf{-5}}{\mathbf{chiliad}}^{\mathbf{2}}/\mathbf{due\; south}$ .

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Theoretical Insights Into Chain Transfer Reactions of Acrylates

Masoud Soroush , Andrew G. Rappe , in Computational Quantum Chemistry, 2019

v.5.2.2 Quantum chemistry versus laboratory experiments

No experimental value (obtained from laboratory experiments) for the charge per unit coefficient of the i:five bluffing reaction of MA was reported. On the other hand, the ane:5 backbiting reaction rate coefficient of MA is believed to be shut to that of nBA [54,121]. This motivated a comparing of Arrhenius parameter values of the 1:five backbiting reaction of MA obtained using breakthrough chemical science methods to experimental values of the aforementioned parameters reported for nBA. Both G4(MP2)-6X and DFT-calculated values of the activation energy of the MA reaction are about 28   kJ   mol⁻¹ college than the experimental value of the same parameter for nBA, whereas the frequency factor estimated with the HR approximation (~10¹²  s⁻ⁱ) is virtually five orders of magnitude college than the experimental value of the aforementioned parameter for nBA. However, in terms of reaction rate coefficient at room T, these theoretical and experimental values are surprisingly in reasonable agreement. Furthermore, these findings are in understanding with those reported by Yu et al. [54] and Cuccato et al. [55,56]. Information technology appears that even the use of the high quality electronic structure calculation method (G4(MP2)-6X) and a sophisticated entropy calculation approach (Hour approximation) does non consequence in eliminating the discrepancy between the theoretical and experimental values of the activation energy and frequency factor. The fact that the DFT-estimated rate constant agrees with the experimental value is attributed to the large error cancellation in electronic structure and entropy calculations when studying liquid-phase reactions in the gas-phase [149]. However, the origin of such a large error cancellation is non clear. Therefore, while it is legitimate to perform first-principles calculations in the gas-phase for reactions actually occurring in liquid-phase (given the good performance of DFT in predicting charge per unit constants), further computational studies using a more realistic model (including solvation model) and a more authentic method for entropy calculations in liquid stage are still required.

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CALPHAD: Adding of Phase Diagrams

In Pergamon Materials Series, 1998

half-dozen.2.two.4 Utilisation of Stacking-Error Energies

Experimental values of stacking-fault energies (SFE) offer a method of providing energy differences between stable and metastable close-packed structures. A rigorous human relationship involves modelling the interface between the error and the matrix, just a good working formula tin can exist established by assuming that this interfacial energy term is constant for a given grade of alloys ( Miodownik 1978c).

(6.thirteen) $\lambda =2(G_{\text{s}}^{\text{f}\text{.c}\text{.c}\text{.}\to \text{c}\text{.p}\text{.h}\text{.}}+\sigma )$

where

(6.14) $G_{\text{southward}}^{\text{f}\text{.c}\text{.c}\text{.}\to \text{c}\text{.p}\text{.h}\text{.}}=\frac{{10}^7}{{\mathrm{North}}^{\mathrm{i}/\mathrm{iii}}}{[\rho /\mathrm{Thousand}]}^{\mathrm{ii}/3}{G}_{\text{m}}^{\text{f}\text{.c}\text{.c}\text{.}\to \text{c}\text{.p}\text{.h}\text{.}}$

${\mathrm{Thousand}}_{\text{south}}^{\text{f}\text{.c}\text{.c}\text{.}\to \text{c}\text{.p}\text{.h}\text{.}}$ is the Gibbs free energy divergence/unit of measurement area between the f.c.c. and c.p.h. phases in mJ grand⁻², σ is the energy of the dislocation interface, p is the density in g cm⁻³, M the molecular weight in grammes and $K_{\text{m}}^{\text{f}\text{.c}\text{.c}\text{.}\to \text{c}\text{.p}\text{.h}\text{.}}$ the Gibbs energy in J mol⁻¹. Eqs (6.13) and (six.14) were originally used to predict the SFE of a wide range of stainless steels, but they accept also been used, in reverse, to estimate values of G ^{f.sc.c.→c.p.h}. of _some f.c.c. elements (Saunders et al. 1988) where they provide values which are in excellent understanding (Miodownik 1992) with those obtained by FP methods (Crampin et al. 1990, Xu et al. 1991).

Although this method is essentially restricted to a particular sub-set of lattice stabilities, it nevertheless provides an additional experimental input, especially in cases where information technology is non possible to admission the metastable phase by other methods. It is therefore disappointing that there are no experimental values of the SFE available for Ru or Bone, which could provide confirmation of One thousand ^{c.p.h.→f.c.c.} obtained by other methods. High SFE values take, withal, been both observed and predicted for Rh and Ir, which is indirect confirmation for a larger variation of $G_{\text{g}}^{\text{f}\text{.c}\text{.c}\text{.}\to \text{c}\text{.p}\text{.h}\text{.}}$ with d-shell filling than proposed by Kaufman and Bernstein (1970).

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Awarding of Fluids

W. Brian Rowe , in Principles of Modern Grinding Technology (Second Edition), 2014

Comparison of Experimental and Predicted Convection Factors

Experimental values of convection factor were estimated from experimental maximum temperature results obtained past Lin et al. (2009) using 36   grand/s bike speed and by Barczak et al. (2010) using 25 and 45   thousand/s wheel speeds. The experiments were conducted on a range of materials including cast iron, general engineering steels and M2 tool steels. The results shown in Figure viii.20 were obtained in a collaborative investigation with Zhang Lei at Liverpool John Moores University (Zhang et al., 2013). Accuracy at the very lowest temperatures depends on sub-micron depth of cut measurements. Further work is ongoing in this region to make up one's mind convection factors. However, the results show that in a higher place the fluid burn down-out temperature, experimental convection factors reduce shut to zero as expected. At very high temperatures, convection factors start to increase over again. This could perchance be due to oestrus radiation from the surface. As temperatures reduce below the burn-out temperature, convection factors announced to become higher than predicted by the LFM. Experimental results confirmed the benefit of high wheel speeds for college fluid convection factors.

Figure viii.twenty. Experimental and predicted fluid convection factors. Higher up 180°C, predicted h _f=0 for a water-based emulsion in the Rowe thermal model.

The predicted values take no account of fluid burn-out but are included for loftier temperatures exceeding burn down-out temperatures to evidence the characteristics of the models. According to the thermal model, convection factors should be taken as zero at burn-out temperatures.

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Mass Transfer and Diffusion

E.50. Cussler , in Encyclopedia of Physical Science and Technology (Third Edition), 2003

III.A Mass Transfer Coefficients

Experimental values of mass transfer coefficients can exist collected every bit dimensionless correlations. 1 drove of these correlations is in Table Two (Cussler, 1977). Because heat transfer is mathematically so like to mass transfer, many affirm that other correlations can be establish by adapting results from the heat transfer literature. While this is sometimes true, the analogy is oft overstated because mass transfer coefficients normally apply across fluid-fluid interfaces. They describe mass transfer from a liquid to a gas or from one liquid to some other liquid. Heat transfer coefficients normally draw ship from a solid to a fluid. This makes the illustration between rut and mass transfer less useful than it might at first seem.

TABLE 2. Useful Correlations of Mass Transfer Coefficients for Fluid–Fluid Interfaces

Physical situation	Bones equation b	Key variables	Remarks
Liquid in a packed tower	$\text{k}{\left(\frac{1}{\mathit{\nu }\text{g}}\right)}^{\mathrm{ane}/3}=0.0051{\left(\frac{{\nu }^0}{a\nu }\right)}^{0.67}{\left(\frac{D}{\nu }\right)}^{0.50}{(\text{a}\text{d})}^{0.4}$	a  =   Packing expanse per bed volume	Probably the best available correlation for liquids; tends to give lower values than other correlations
		d  =   Nominal packing size
	$\frac{k\text{d}}{\text{D}}=25{\left(\frac{\text{d}{\nu }^0}{\nu }\right)}^{0.45}{\left(\frac{\mathit{\nu }}{\text{D}}\right)}^{0.5}$	d  =   Nominal packing size	The classical result, widely quoted; probably less successful than to a higher place
	$\frac{\text{m}}{{\nu }^0}=\alpha {\left(\frac{\text{d}{\nu }^0}{\nu }\right)}^{-0.3}{\left(\frac{D}{\nu }\right)}^{0.5}$	d  =   Nominal packing size	Based on older measurements of height of transfer units (HTUs); α is of gild one
Gas in a packed belfry	$\frac{\text{k}}{a\text{D}}=3.6{\left(\frac{{\nu }^0}{\text{a}\nu }\right)}^{\mathrm{0.lxx}}{\left(\frac{\nu }{\text{D}}\right)}^{1/3}{(\text{a}\text{d})}^{-2.0}$	a  =   Packing area per bed volume	Probably the best available correlation for gases
	$\frac{\text{k}\text{d}}{\text{D}}=1.2{(1-\in )}^{0.36}{\left(\frac{\text{d}{\nu }^0}{\nu }\right)}^{0.64}{\left(\frac{\nu }{\text{D}}\right)}^{\mathrm{i}/3}$	d  =   Nominal packing size
		d  =   Nominal packing size	Again, the most widely quoted classical result
		ɛ   =   Bed void fraction
Pure gas bubbles in a stirred tank	$\frac{\text{k}\text{d}}{\text{D}}=\mathrm{0.xiii}{\left(\frac{(\text{P}/\text{5}){\text{d}}^4}{\rho {\nu }^{\mathrm{iii}}}\right)}^{1/\mathrm{iv}}{\left(\frac{\nu }{\text{D}}\right)}^{\mathrm{one}/3}$	d  =   Bubble diameter	Note that k does not depend on bubble size
		P/V  =   stirrer power per volume
Pure gas bubbles in an unstirred liquid	$\frac{\text{k}\text{d}}{\text{D}}=0.31{\left(\frac{{\text{d}}^3\text{g}\Delta \rho /\rho }{{\nu }^{\mathrm{two}}}\right)}^{\mathrm{i}/3}{\left(\frac{\nu }{\text{D}}\right)}^{1/\mathrm{iii}}$	d  =   Bubble diameter	For modest swarms of bubbles rising in a liquid
		Δρ   =   Density difference between gas and liquid
Big liquid drops rise in unstirred solution	$\frac{\text{k}\text{d}}{\text{D}}=0.42{\left(\frac{{\text{d}}^{\mathrm{three}}\Delta \rho \text{yard}}{\rho {\nu }^2}\right)}^{\mathrm{one}/3}{\left(\frac{\nu }{\text{D}}\right)}^{0.5}$	d  =   Chimera diameter
		Δρ   =   Density departure between bubbles and surrounding fluid	Drops 0.three-cm diameter or larger
Pocket-size liquid drops ascension in unstirred solution	$\frac{\text{k}\text{d}}{\text{D}}=1.13{\left(\frac{\text{d}{\nu }^0}{\text{D}}\right)}^{0.8}$	d  =   Drop diameter	These small drops behave like rigid spheres
		v 0  =   0 Driblet velocity
Falling films	$\frac{\text{k}\text{z}}{\text{D}}=0.69{\left(\frac{\text{z}{\nu }^0}{\text{D}}\right)}^{0.5}$	z  =   Position along movie	Frequently embroidered and embellished
		v 0  =   Boilerplate film velocity

^a The symbols used include the post-obit: D is the diffusion coefficient; g is the acceleration due to gravity; grand is the local mass transfer coefficient; five ⁰ is the superficial fluid velocity; and ν is the kinematic viscosity.

b

Dimensionless groups are as follows: dv/ν and 5/aν are Reynolds numbers; ν/D is the Schmidt number; d ³ chiliad(Δρ/ρ)ν² is the Grashoff number. kd/D is the Sherwood number; and k/(νg)^one/3 is an unusual form of Stanton number.

The correlations in Table Two are most oft written in dimensionless numbers. The mass transfer coefficient k, which about often has dimensions of velocity, is incorporated into a Sherwood number Sh

(35) $\text{S}\text{h}=\frac{\text{k}\text{d}}{\text{D}}$

where d is some characteristic length, like a pipe diameter or a film thickness, and D is the aforementioned diffusion coefficient which we talked nearly earlier. The mass transfer coefficient is most frequently correlated as a function of velocity, which ofttimes appears in a Reynolds number Re

(36) $Re=\frac{\text{d}\upsilon }{\nu }$

where 5 is the fluid velocity and ν is the kinematic viscosity; in a Stanton number St

(37) $\text{Southward}\text{t}=\frac{\text{m}}{\upsilon }$

or as a Peclet number Pe

(38) $\text{Pe}=\frac{\text{d}\upsilon }{\text{D}}$

The variation of mass transfer coefficients with other parameters, including the diffusion coefficient, is often not well studied, and then the correlations may take a weaker experimental basis than their frequent citations would suggest.

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Devices and Applications

C.R. Becker , ... S. Sivananthan , in Comprehensive Semiconductor Science and Engineering, 2011

6.04.5.iii Optical Properties

Experimental values ( Schmit and Stezter, 1969; Hansen et al., 1982; Laurenti et al., 1990) for the bandgap of Hg_{1   − x} Cd _x Te together with empirical fits of the data (Hansen et al., 1982; Laurenti et al., 1990) are plotted versus 10 for 77   Thou in Figure xi . The empirical relationship of Hansen et al. (1982)

(5) $E_{\mathrm{one\; thousand}}=-0.302+1.930\mathrm{ten}+5.35\times {\mathrm{ten}}^{-4}T(1-2x)-0.810x^{\mathrm{two}}+0.832{\mathrm{ten}}^3$

in units of eV was based on data for Hg_{1   − 10} Cd _x Te with x values upwards to 0.twoscore. These data were supplemented with values for larger Cd concentrations by Laurenti et al., 1990 resulting in

(6) ${\mathrm{Eastward}}_{\text{one thousand}}=-0.303(\mathrm{i}-x)+\mathrm{ane.606}x-0.132x(1-x)+[\mathrm{vi.three}(1-x)-\mathrm{three.25}x-5.92x(1-x)]\times {10}^{-4}{T}^2/(\mathrm{xi}(1-\mathrm{ten})+\mathrm{78.seven}x+T)$

too in units of eV. The empirical equation (five) arguably agrees meliorate with experimental information for ten  <   0.5 at all temperatures, whereas Equation (6) is improve for x   >   0.5 due primarily to the authors' analysis of the data in light of 3D exciton theory of directly allowed transitions which is of import for Cd concentrations larger than approximately 0.five. In fact, values for the CdTe binary according to Equation (5) are almost 42 and 15   meV larger, and 30   meV smaller than accepted experimental values at 4, 77, and 300   K, respectively.

Figure 11. Experimental bandgaps of Hg_{1   − x} Cd _x Te (symbols) as well equally the empirical fits of the information from Hansen et al. (1982) (solid line) and Laurenti et al. (1990) (dashed line) as a office of x at 77   M. Experimental data are from Hansen et al. (1982) (squares), Schmit and Stezter (1969) (circles), and Laurenti et al. (1990) (diamonds).

With decreasing Cd concentration, the band structure of Hg_{one   − ten} Cd _x Te becomes more nonparabolic and the assimilation coefficient tin can no longer be described past the normal square root relationship

(seven) $\alpha \propto {(E-E_{\text{1000}}(x,T))}^{0.5}$

This is dramatically demonstrated by the theoretical absorption coefficient α spectra for Hg_{1   − 10} Cd _x Te plotted in Figure 12 which can be satisfactorily reproduced with Equation (7) only for 10 values approaching 1.0, due to the pronounced nonparabolicity of the Hg_{i   − x} Cd _x Te ring structure. The absorption coefficients were calculated by ways of an (8   ×   eight) k · p model (Becker et al., 2000), which is very practiced in reproducing experimental α spectra, as is clearly demonstrated in Figure 13 .

Effigy 12. Theoretical absorption coefficient for the Hg_{i   − x} Cd _x Te alloy with x values of 0.twenty, 0.25, 0.thirty, 0.forty, 0.50, 0.60, 0.seventy, 0.80, 0.xc, and ane.00 at 295   K.

Figure 13. Experimental (thick lines) and theoretical (thin lines) absorption coefficient, α, for a HgTe/ Hg_{1   − ten} Cd _ten Te SL and a Hg_{i   − x} Cd _x Te alloy with a bandgap near 60   meV or a cutoff wave length of about 20μm at 40   K. The two theoretical spectra for the alloy are for 2 different electron concentrations and the corresponding Fermi energies.

Figure 13 points out two pronounced advantages of a SL based on HgTe and CdTe compared to the Hg_{one   − x} Cd _x Te alloy or indeed any other material in the far infrared region. These two benefits include: (one) the SL has a much steeper absorption coefficient and (2) consequently, nearly an club of magnitude larger absorption coefficient equally well as a significantly lower Burstein–Moss shift (Burstein, 1954; Moss, 1954); for a SL it is an order of magnitude lower for a cut-off wavelength of twenty μm at 40   K. The latter advantage is due to the fact that the electron effective mass k* for an alloy is smaller than the corresponding geometric mean of the parallel and perpendicular electron constructive masses for a SL.

Two additional meaning advantages of the SL are the capabilities to reduce leakage currents also every bit to suppress Auger recombination through the advisable option of SL parameters, that is, band structure engineering. Plain, they are important in improving devices in the far infrared region by an appreciable reduction in tunneling currents and increase in carrier lifetimes.

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SURFACE AND INTERFACE ANALYSIS AND Backdrop

Vladislav Domnich , Yury Gogotsi , in Handbook of Surfaces and Interfaces of Materials, 2001

2.two Depth-Sensing Indentation

Experimental values of the phase transformation pressures may be assessed through the depth-sensing (nano)indentation technique, which allows loftier-resolution in situ monitoring of the indenter displacement as a office of the practical load. Changes in a cloth'south specific volume or mechanical properties during a phase transition are revealed every bit characteristic events in the load-deportation curve. The formation of a new phase under the indenter may consequence in the yield pace ("popular-in") or the modify in slope ("elbow") of the loading curve; a sudden displacement discontinuity ("pop-out") or an elbow in the unloading bend may be indicative of the reverse transition. In cyclic indentation, boosted information can be extracted from the broad or asymmetric hysteresis loops or from the specific features in the reloading curves [38].

In one case a specific event in the load-displacement curve has been associated with a particular phase transition, the pressure at which it occurs can be estimated by considering the elastoplastic beliefs of the material under the indenter. For the signal-force contact, the Sneddon's solution [39] to the trouble of the penetration of an axisymmetric punch into an elastic half space predicts the following relation between the applied load P and the indenter displacement h:

(ten) $P=\alpha h^2$

where the parameter α is determined by indentation geometry and the mechanical properties of the specimen [39].

As described in the previous department, including plasticity in the modeling of indentation contact is a complex problem and analytical solutions are non hands obtained [32]. Fortunately, in almost cases, at least the upper function of the unloading curve is rubberband, leading to the following modified Sneddon's relation [40]:

(xi) $P=\alpha {(h-h_f)}^m$

where the residual plastic deformation h_f (Fig. seven) is introduced to retrieve the rubberband part of the indenter displacement during unloading.

Fig. 7. (a) Load-displacement curve of a typical elastoplastic textile and (b) the schematic of the indentation model of Oliver and Pharr [40]. S—contact stiffness; h_c —contact depth; h _max—indenter deportation at peak load; h_f —plastic deformation after load removal; h_s —deportation of the surface at the perimeter of the contact.

The power exponent m in Eq. (11) needs special attention. All-encompassing nanoindentation studies performed by Oliver and Pharr [40] on materials with various mechanical backdrop implied that m is a fabric abiding and has the values in the range of 1.0 to two.0. In fact, the routine analysis of nanoindentation data begins with the decision of the parameters α and thou for a particular experiment by numerically plumbing equipment the measured unloading curve. This suggests deviations from the Sneddon's solution m = 2; (Eq. (10)) in real cases. As shown by Sakai et al. [41], about commercially bachelor indentation exam systems (including that of [forty]) are designed in such a mode that the load frame compliance and mechanical contact clearances inevitably and significantly modify the load-displacement data. In contrast, for a "strong" indentation system, the indenter deportation is indeed proportional to the square root of the applied load and the Sneddon's solution (Eq. (x)) is preserved in this example [41].

Oliver and Pharr [40] proposed a procedure to assess the average contact pressure at summit load P _max from the experimental load-deportation curves by determining the projected contact area A, which is a function of the corresponding maximum contact depth h_{c ,max}. In general, at a given load P, the contact depth h_c tin be determined equally the difference betwixt the indenter displacement h and the surface deflection at the perimeter of indentation h_s (meet Fig. 7). Assuming that the elastic deflection of the sample surface h_s is directly proportional to the foursquare root of the indentation load P, Novikov et al. [42] developed a method to assess the instantaneous contact depth h_c from the maximum surface deflection at peak load, provided h_{south ,max} has been determined by the Oliver-Pharr's technique. This allows estimation of the average contact pressure p_k for both, loading (elastoplastic) and unloading (elastic) segments only every bit

(12) $p_m=\frac{P}{A\left(h_c\right)}$

The quantification of contact pressures in spherical indentation is based on the indentation model of Field and Swain [43]. The process is like to the point-strength indentation and includes the evaluation of the contact radius at a given load (a_c ) from its value at height load (a_{c ,max}) The mean contact force per unit area is then institute as [43]

(13) $p_g=\frac{P}{\pi a_c^{\mathrm{two}}}$

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SURFACE AND INTERFACE PHENOMENA

B.F. Dorfman , in Handbook of Surfaces and Interfaces of Materials, 2001

6.4 Groovy Threshold

The experimental values of the bully threshold strongly depend on the shape and properties of the indenter. Accordingly, comparative measurements of QUASAM and other materials with the same Vickers indenter accept been conducted. Tabular array VIII shows the results.

Table Eight. Swell Threshold: Comparative Measurements of QUASAM and other Materials with the Same Vickers Indenter ^a

Material	Bang-up threshold (N)	Hardness Hv , (GPa)	Reference data
QUASAM (ranges for twenty		13 ≤ H5 ≤ 45	—
freestanding samples):
Normal direction, growth side	5 ≤ wc ≤ x, 10 ≤ wdue south ≤ 20, wr ≥ 20
Normal management, substrate side	3 ≤ wc ≤ vDue north, 7 ≤ ws ≤ 10, wr ≥ 20
In plane	ane–6 ≤ westwardc ≤ 3, 5 ≤ wdue south ≤ 10, wr ≥ 3
Silicon (100)	wc = 0.38(0.33**)	10.eight±0.5	11.iii [84]
Plate polished glass, optical quality (window for vacuum chambers)	due westc . = 2.2, wsouth = ii.4, wr = two.6	6.2	5.5 [84] soda-lime glass
Microcover drinking glass, 170 μchiliad	wr = 1.1	5.5
Sight glass for microscopy	due westr = 0.73–0.78	5.4
Fused quartz, polished, optical quality	westr = 1.0–1.7	viii.9±0.i	viii.9 [96]
Quartz, natural crystal	wr = 0.7	10.three	1360 (Knoop) [84]
Topaz, natural crystal	wr = 0.65	12.6	1340(Knoop) [96]

a

w_c —Conical cracks, w_s —limited microsplitting, w_r —radial cracks.

The freestanding samples of QUASAM were studied in three directions: in the normal direction from the growth side, in the normal management from the interface side (later on the silicon substrates accept been etched off), and in parallel to substrate directions (using the apartment cross-fractures).

The values indicated for QUASAM in the normal management from the growth side are consistent with a long-term systematic examination (about 3500 measurements total). The values for other materials are the result of thirty measurements for each fabric (3 specimens × 10 measurements for each specimen). Comparative resistance of QUASAM and silicon to crack nucleation and propagation is also illustrated past Figure xiv.

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Effect of nitrogen contamination by crucible encapsulation on polycrystalline silicon fabric quality

Due south. Binetti , ... A. Musinu , in C,H,Northward and O in Si and Characterization and Simulation of Materials and Processes, 1996

3.2 IR spectroscopy and SIMS measurements

The experimental values of the oxygen and carbon concentrations of the central samples are reported in Table 1. The presence of a vertical and radial concentration gradient is due to the different segregation coefficients of oxygen and carbon and to the presence of a horizontal and vertical temperature gradient in the ingot during the cooling.

Tabular array one. Oxygen and carbon concentrations of lateral and primal samples

Samples	[O] (ppm at.)	[C] (ppm at.)
Lateral
LT	1.0 ± 0.6	15.8 ± 0.half-dozen
LM	two.7 ± one.two	10.8 ± 0.viii
LB	5.v ± 0.8	6.7 ± 0.7
Fundamental
CT	<0.5	17.eight ±0.6
CM	2.1 ± 0.1	11.8 ± 0.8
CB	4.6 ± 0.i	8.six ± 0.7

From IR spectra we did not succeed in detecting the presence of nitrogen or nitride precipitates in regions where TEM measurements showed the presence of nitride precipitates (encounter adjacent section).

In order to observe a possible excess of B, C, N and O shut to crystallographic defects or in the neighbourhood of ingot edges, we also carried out SIMS measurements on a few selected samples. These measurements indicated only that cosegregation of carbon and oxygen is favoured close to loftier resistivity GBs (see Fig. iii) while infragrain oxygen and carbon precipitates are observed corresponding to twinned regions, in good understanding with our previous results [9].

Fig. iii. SIMS maps of (a) oxygen precipitates and (b) carbon precipitates respective to a GB, indicated with a dotted line. The diameter of the map is 150 μm.

No evidence was found, presumably as a issue of instrumental sensitivity limits, of nitrogen or nitride aggregates at high resistivity GBs.

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Thermal Conductivity and Specific Heat

David R.H. Jones , Michael F. Ashby , in Engineering Materials 1 (Fifth Edition), 2019

32.two Thermal Conductivities and Specific Heats

Estimate experimental values for K, C, and λ are shown in Table 32.1. These are generally measured at, or fairly close to, 300   K. Since K, C, and λ tin change with temperature, in any thermal blueprint problem it may be necessary to obtain experimental data for the particular temperature range under consideration.

Tabular array 32.1. Information for Thermal Conductivity (G, in W   one thousand^{−   one}  K^{−   one}), Specific Heat (C, in J   kg^{−   i}  K^{−   1}), and Thermal Diffusivity (λ  = Yard/ρC, in mⁱⁱ  s^{−   1}; ρ  =   Density in kg   m^{−   iii})

Material	K	C	λ (Average)
Metals
Argent	425	234	1.seven   ×   ten−   four
Zinc	120	390	iv.3   ×   10−   5
Zinc die-casting alloy	110	420	iii.ix   ×   10−   5
Magnesium	156	1040	8.half dozen   ×   10−   v
Aluminum	240	917	ix.7   ×   ten−   5
Aluminum alloys	130–180	900	6   ×   10−   five
Copper	397	385	1.2   ×   10−   iv
Copper alloys	20–210	400	three   ×   ten−   five
Iron, carbon steel, low-alloy steel	40–78	480	1.vi   ×   10−   5
High-blend steels	12–xxx	500	5   ×   10−   half dozen
Stainless steels	12–45	480	8   ×   x−   6
Nickel	89	450	2   ×   10−   5
Superalloys	11	450	three.1   ×   ten−   6
Titanium	22	530	9.2   ×   10−   6
Ti-6Al 4V	6	610	ii.2   ×   x−   6
Controlled-expansion alloys
Kovar (Nilo-1000), 54Fe29Ni17Co	17	460	4   ×   10−   6
Invar, 64Fe36Ni	thirteen	515	3   ×   10−   6
Ceramics and glasses
Cement and (un-reinforced) concrete	one.viii–2	1550	five   ×   10−   seven
Soda glass	i	990	4   ×   10−   7
Alumina	25.six	795	8   ×   10−   6
Zirconia	i.5	670	4   ×   10−   7
Limestone	2.i	920	8   ×   10−   7
Granite	3	800	i.four   ×   x−   vi
Silicon carbide	4–twenty	740	5   ×   x−   6
Borosilicate glass	i	800	half dozen   ×   10−   7
Silicon nitride	ten	650	half-dozen   ×   10−   6
Porcelain	i	800	5   ×   ten−   7
Diamond (natural, high purity)	2500	510	1.4   ×   10−   3
Polymers (thermoplastics)
Polypropylene (PP)	0.2	1900	ane   ×   10−   seven
Polyethylene, high density (HDPE)	0.iv	2100	2   ×   x−   7
PTFE	0.25	1050	1   ×   ten−   seven
Nylons	0.2–0.25	1900	one   ×   10−   seven
Polystyrene (PS)	0.1–0.fifteen	1400	8   ×   x−   8
Polycarbonate (PC)	0.2	1100	1   ×   x−   seven
PMMA (Perspex)	0.2	1500	one   ×   ten−   7
Polyvinylchloride, unplasticized (UPVC)	0.xv	one thousand	1   ×   10−   7
Polyetheretherketone (PEEK)	0.25	320	6   ×   ten−   7
Polymers (thermosets/resins)
Epoxies	0.two–0.five	1800	2   ×   x−   vii
Polyesters	0.two–0.24	2000	ane   ×   10−   vii
Phenol formaldehyde	0.12–0.24	1600	1   ×   10−   7
Polymers (rubbers/elastomers)
Silicone	0.fourteen	1200	i   ×   10−   7
Nitrile butadiene (NBR)	0.24	1350	1   ×   10−   vii
Fluorocarbon (Viton)	0.2	950	1   ×   10−   7
Polyisoprene, polybutadiene	0.ane	2000	5   ×   10−   eight
Polymer-matrix composites
Glass-filled nylons (30% glass by weight)	0.3	1600	1   ×   ten−   7
Tufnol (paper or woven fabric laminated phenolic resin)	0.36	1500	2   ×   10−   7
Porous materials
Forest	0.05–0.25	2500	2   ×   10−   vii
Cork	0.04	1900	one   ×   10−   7
Mineral wool	0.04	1000	2   ×   ten−   six
Foams (PUR, phenolic)	0.02	1650	three   ×   10−   7
Expanded PS	0.036	1400	1   ×   10−   half-dozen

Some pure metals have large values of Thousand (eastward.thousand., silver, copper, aluminum), only alloying with other metals usually reduces K considerably (e.g., some copper alloys, some loftier-alloy and stainless steels, nickel-based superalloys, Ti-6Al4V). K values for ceramics and glasses are mostly 2 orders of magnitude less than for metals (although alumina, silicon carbide, and silicon nitride overlap with metals). Yard values for polymers are an society of magnitude less than for ceramics, and for porous materials another order of magnitude less again. In that location is much less variation in the specific heats, although polymers tend to accept C values roughly two to four times those of other materials. λ values range from ≈   10^{−   7} (polymers) to ≈   ten^{−   4} (some pure metals). (High-purity, natural diamond is an extraordinary outlier, with a K value v times, and a λ value x times, those of copper or silver.)

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How To Find Experimental Value,

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