# a) A crystal is a solid whose atoms or ions are arranged in an orderly, repeating pattern in 3-dimensions. Crystals are represented by repeating subdivisions called 'unit cells', which incorporate the geometrical properties of the entire crystal. The arrangement of the crystal enables the atoms to be most closely packed with maximum amount of primary bonds and minimal energy of the aggregates; it is for this reason that the atoms are arranged in such a way.

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Nov 15, 2013 (4 years and 6 months ago)

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1

BMED 2100

Homework #1:

Due Date: February 3
rd

Beginning of Class

1
. a) In the solid state, each primary class of materials exhibit varied types of atomic structure.
What is a crystal

(1 point)

and why do atoms arrange themselves in these configurations

(1
point)
?

b) For metals, describe the three major types of crystal structures, including the number of
atoms in each unit cell, the atomic packing factors (packing density), and the coordinatio
n
numbers

(1 point for each type of crystal structure)
.

a) A crystal is a solid whose atoms or ions are arranged in an orderly, repeating pattern in
3
-
dimensions. Crystals are represented by repeating subdivisions called 'unit cells', which
incorporate
the geometrical properties of the entire crystal. The arrangement of the crystal
enables the atoms to be most closely packed with maximum amount of primary bonds and
minimal energy of the aggregates; it is for this reason that the atoms are arranged in su
ch a
way.

b)
The first type of crystal structure exhibited by metals is the BCC (Body centered cubic),
with the unit cell consisting of a net total of 2 atoms, with each atom having 8 neighboring
atoms
-

coordination number = 8. The atomic packing factor

(Total volume of the
atoms/volume of a unit cell) is .68, and this number is representative of a 68% density of
atoms packed into a single unit cell.

The other two types of crystal structures exhibited by metals are FCC (Face centered
cubic), with a net
total of 4 atoms in each unit cell, and HCP (Hexagonal close packed),
whose net total of atoms equals 6. In both types of crystal structure, each atom is
surrounded by 12 neighboring atoms and the atomic packing factors being equal to .74;
again, the num
ber is representative of 74% density of atoms in the unit cell.

2

2.
a) Express Hooke's Law for both tensile/compressive and

(1 point for each
equation)
.
b)
Draw an elastic region stress
-
strain curve for each comparing Al
2
O
3

and gold

(2
graphs

1 point for correctly labeling the graph axes, 1 point for correct placement of the curves
with respect to one another

total of 4 points possible)
.

Hooke's law can be expressed in quantitative terms as such:

σ = E ε (Tensile or
compressive
),
where
σ
represents stress, E represents Young's/elastic
modulus, and
ε
represents strain.

τ = G γ

(Shear), where
τ
represents stress, G represents Shear modulus, and
γ

represents
strain.

3

3. Although many materials
are able to demonstrate elasticity, this behavior is not indefinite
under applied stress; hence, microscopic defects are eventually introduced into the material. a)
Compare brittle fracture with plastic deformation (1 point). What are different factors th
at can
contribute to the occurrence of these phenomena (1 point)?

can be resultant of plastic deformation (1 point)?

a) In brittle fracture, the application of tensile or shear stress reaches a point at which
sudden materia
l failure occurs, known as the fracture stress. Until this point, the stress
strain curve does not deviate from a straight line, and this behavior is typical of materials
such as glass, ceramics, very hard alloys and some polymeric materials. Some facto
rs that
can influence the occurrence of brittle fracture are the number and size of material defects
and material porosity.

Plastic deformation occurs after the yield strength (.2% plastic strain) is exceeded but
before fracture of the material is reached
. Once plastic deformation starts, the strains
produced are much greater than those during elastic deformation and are no longer
proportional to the stress on the material. Elastic deformation involves straining of the
microstructure such that the atoms
are displaced only slightly by reversible stretching of
the interatomic bonds. By contrast, plastic deformation involves irreversible motion of the
atoms under applied stress to new locations in the crystal structure; hence, true plastic
deformation is on
ly possible in materials that undergo metallic bonding.

b)
Plastic deformation can be useful in shaping metallic materials and is associated with the
material being ductile or malleable. The permanent/plastic strain exhibited up to fracture
by a
material is a measure of its ductility, and this property can be used in strengthening
techniques of the material. Such techniques can involve increasing the yield strength by
reducing grain size. During the fabrication process, introduction of alloys, m
ultiphase
microstructures, and working the material under various temperatures (heat treatment,
which can increase ductility but reduce strength, and working materials at room
temperature to increase the strength by flattening the grains but reducing ducti
lity) can all
contribute to the mechanical characteristics of a certain material.

4

4
.
A contact angle analysis is a technique often utilized to determine the wettability of a material
surface (whether a material is hydrophobic or hydrophil
ic). If a water droplet is used for this
analysis and given that there are three biomaterials of varying hydrophobicity (A = Very
hydrophobic, B = Very hydrophilic, C = Somewhat hydrophilic), sketch the surface of these
materials and how the water droplet

might look upon interacting with these surfaces

(1 point for
each sketch

3 total points)
.

5

5
. What are the two general principles that guide surface characterization of all material types (1
point for each principle)?
used to characterize biomaterial surfaces (1 point for an advantage and one point for a

4 total points).

The first principle that guides surface characterization is that a test

must account for the
fact that any surface characterization method has the potential to alter or damage the
surface of a material specimen. The second principle that guides characterization of a
surface is resultant of the potential for artifacts and ina
ccuracies of testing methods.
Because it is possible for these errors to arise, it is essential that more than one test should
be performed in order to best characterize a material. Also, each test performed should
result in data that are corroborative an
d exhibit similarly predicted results.

Contact angle analysis

liquid wetting of a surface used to estimate the surface energy.
Can analyze a depth of 3
-
20A, low spatial resolution (1mm), sensitivity can be altered in
response to chemistry performed, an
d low cost.

ESCA (XPS)

X
-
rays induce electron emission of characteristic energy. Can analyze depth
of 10
-
250A, spatial resolution of 10
-
150um, .1% at sensitivity, but very expensive.

Auger electron spectroscopy

a focused electron beam is used to sti
mulate Auger electron
emission. Can analyze a depth of 50
-
100A, spatial resolution of 100A, .1 atom %
sensitivity, but very expensive.

SIMS

Secondary Ion Mass Spectrometry

Ion bombardment sputters secondary ions
from the surface. Can analyze a dept
h of 10A
-
1um, spatial resolution of 100A, very high
analytical sensitivity, but very expensive.

FTIR
-
ATR

resultant excitation. Can analyze to depth of 1
-
5um, spatial resolution o
f 10um, 1mol%
analytical sensitivity, and moderately expensive.

STM

Quantum tunneling is measured between a metal tip and a conductive surface. Can
analyze to a depth of 5A, spatial resolution of 1A, has analytical sensitivity of single atoms,
and is m
oderately expensive.

SEM

Secondary electron emission induced by a focused electron beam that is spatially
imaged. Can analyze a depth of 5A, spatial resolution of 40A, high (but not quantitative)
analytical sensitivity, and is moderately expensive.

6

6
. You have been hired as a biomaterials consultant for a medical device company to provide
input on material selection for a number of devices in the R&D pipeline. Using Table 1 on page
69 as a reference, choose an appropriate polymer to recommend for

use in the following
devices. Provide reasoning based upon the mechanical properties listed.

a.

Bone cement (must resist deformation under large compressive forces)

(1 point)

Example: PMMA

b.

Catheters/medical tubing (must be somewhat flexible and able to be
extruded)

(1
point)

Example: PE

c.

Blood transfusion bags (must be pliable yet able to withstand the high heats of
sterilization without melting)

(1 point)

Example: PVC

7
. You are given 197.3 grams of a batch of polytetrafluoroethylene (PTFE) with the

following
distribution data:

Chain length (# repeating
units)

Numerical fraction of chains in sample

(moles species/total moles)

500

.3

750

.4

1,000

.2

1,250

.1

a.
What is the molecular weight of each species? (Hint: look at page 71.) (1 point

each

4
points total)
.

Chain length (# repeating
units)

Molecular weight of species (g/mol)

500

49,999

750

74,985

1,000

99,980

1,250

124,975

7

b. What is the number average molecular weight of the sample

(1 point)
?

M
n

=
77,490 g/mol

c. The
polydispersity index (PI) of the sample is 2.65. What the weight average molecular
weight of the sample

(1 point)
?

M
w

= 205,340 g/mol

8
.
Based upon the structures of the repeating units shown on page 71, rate the degree of
crystallization expected in a

sample of each of the following polymers: polyethylene (PE)
homopolymer, polyvinylchloride (PVC) homopolymer, Poly (2
-
hydroxyethyl
-
methacrylate)

(1 point for correct comparison, 1 point for
proper reasoning

two total points)
.

Most
-
>least: PE, PVC, poly(HEMA)