6. Medical implants are often made of either titanium, resin or ceramics. A. Com

Question

6. Medical implants are often made of either titanium, resin or ceramics. A. Compare the following for the volume of expansion: i) natural tooth material (alpha = 8.3 x10^-6/C), ii) resin (alpha = 81x10^-4/C) and iii) titanium alloys (alpha = 25x10^6/C) for a tooth approximated by a cylinder with radius 0.50 cm and height of 2.0 cm (1.( cm root and 1.0 cm exposed tooth) at 37C in comparison to the pre-implant room temperatur of 20 degree C. B. Next compare the expansion volume for the tooth or implant upon drinking a hot liquid, i.e. between 37 degree C and 90 degree C. C. If the teeth placement leaves a gap of 0.5 mm between teeth, would any of the materials cause buckling of the teeth?

Explanation / Answer

(A):

T initial = 20 degree C

T final = 37 degree C

Volume = pi*r^2 * h

V = pi* (5*10^(-3))^2 * 2*10^(-2)

V = 1.57*10^(-6) meter cube

delta T = T final - T initial

delta T = 17

delta V = alfa * V * delta T

(i): for natural tooth material

alfa (natural tooth material )= 8.3*10^(-6) / C

delta V (natural tooth material ) = 8.3*10^(-6) * 1.57*10^(-6) * 17

delta V (natural tooth material ) = 221.5270 * 10^(-12) meter cube

(ii): for resin

alfa (resin) = 81*10^(-6) /C

delta V (resin) = 2161.9*10^(-12) meter cube

(iii): for titanium alloys

alfa (titanium alloys) = 25*10^(-6) /C

delta V (titanium alloys) = 667.25*10(-12) meter cube

(B): consedering the maximum temprature 90 degree C

delta T = 70

(i): for natural tooth material

alfa (natural tooth material )= 8.3*10^(-6) / C

delta V (natural tooth material ) = 8.3*10^(-6) * 1.57*10^(-6) * 70

delta V (natural tooth material ) = 912.17 * 10^(-12) meter cube

(ii): for resin

alfa (resin) = 81*10^(-6) /C

delta V (resin) = 8901.9*10^(-12) meter cube

(iii): for titanium alloys

alfa (titanium alloys) = 25*10^(-6) /C

delta V (titanium alloys) = 2747.5*10(-12) meter cube

(C):

if teeth leaves a gap of 0.5 mm then it's expansion has margin or 0.5 mm radius.

volumetric margin is = pi* (5.5*10(-3))^2 * 2*10(-2) - pi* (5.5*10(-3))^2 * 2*10(-2)

volumetric margin = 389868 * 10^(-12) meter cube

this shows in none of the three cases teeths would b buckled.

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