Formula Sheet: Materials Physics
Mechanical properties: stress o=F/A, strain ¢=(I-lo)/lo=Al/lo , stress-strain curve o = f(e) = Ee
shear stress t=F/A, shear strain Ab/h=tan y, t = G tan y, compressibility AV/Vo = -Kp = -p/K
K = E/(3(1-2v)) G=E/(2(1+v)) E/G = 9/(3+(G/K))
Elastic energy Weer= E = J. F(s)ds = i Dsds = +2 DS? orE=222E02 = +2 8¢?
Thermal properties: Heat capacity C = AQ/AT, specific heat capacity c = AQ/(mAT)
Thermal expansion | - lo = (Ti - To), AV = yYAT
Heat conductivity and heat transition: = =O = -as |grad(T)| = ASAT = as (T1—T2)
H. transfer: “2 = @ = @AAT = aA(T1—T2), h. transition: 2 = Q =kAAT =kA(T1-T2)
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Stefan-Boltzmann law: = oAT* , Wien‘s displacement law: “"** —
T
Optical properties: Snell‘s law: nisin(c) = nasin(B),
Some of Fresnel‘sj laws: . reflecti.on coeff. % =__ ttaann((aat—pB))
3 _= __siSnn(was-fp)y
transmission coeff. ts=r;+1 , natp=ni(rp+1) , reflectivity p=r’, transmittivity t=(n2cosB)/(nicosa)t?,
Brewster angle: tan Og =n2/Mn:. critical angle: sin &¢ =n2/n1, spectr. reflectivity RA) = Le (A)
Lambert-Beer law: J,(x,A) =1,(A) exp|-@(A)x| I,(x, A) = Ip(A)10~-?
I,(A)
-Ig(I/Iy) = ODBel
Abbe number: v=(n(green)-1)/(n(blue)-n(red))
Electrical properties: resistance R = pL/A, electrical conductivity o = 1/p, p(T) = p(To)[1 + B(T — To)]
Current densityj = I/A = Q/tA = neAL/At = nev, electron mobility v = pteE, Lorentz force:
F = q(@ x B), capacity ofa plate capacitor Cy = & “, E= ErE05 flux density D=e,e9E
Susceptibility ye = €-1, P=E CeE,
Magnetic properties: MF of a straight wire: H(r) = Up “ey , coil: H = ~ magn. flux density:
Bo = HoH, B = uo,, B= uo + uM =po(H+M) = uo(H+%mH) = woh + xm)
Faraday effect: 8 = VdB
Metallic materials: Force on charged particle in field E: Fo = qE = mo drift velocity: vp = =TF
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Conductivity o = = = &= thermo voltage Urn = (Ss — Sa) DT
Magnetic materials: magn. moment:m = IAa ,m = mug, = Ge be;
Etchin. g: Ani° sotropy: A= 1 — —v#27@1 4 = 1 — 44Vv.
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