CALCULATION
OF MAXIMUM
ALLOWABLE PRESSURES ON
CIRCULAR WINDOW MATERIALS
Calculation
of maximum pressure will depend upon a number of
user selectable parameters. For instance, the window
material, window size, flange size and a safety
factor all may be varied depending upon application.
To
calculate maximum allowable pressure, we must assume
that the maximum stress in a uniform circular plate
is given by the equation:
where
k is a constant, the value for which depends upon
whether or not the window is clamped — use
0.75 for clamped windows and 1.125 for unclamped
(See Fig. 2). Smax is the maximum stress, D is the
window diameter under pressure (ie, the portion
of window not supported by the flange as shown in
the schematic in Figure 2), P is the load (expressed in psi), and t
is the thickness of the window material. In the formula solving for t, the window diameter D can be expressed in any unit of measure such as mm or inches. To avoid
plastic deformation a safety factor must be introduced
where SF is a safety factor and Fa is apparent elastic
limit for the material itself. Where apparent elastic
limit is not available, use yield stress. Allowing
for a safety factor (SF), the equations for calculation
of maximum allowable pressure and for minimum window
thickness (t) where the operating pressure (P) is
known are:
The
apparent elastic limits of some IR optical materials
are listed below:

ATR
SPECTROSCOPY
The
formulae set forth below are useful for ATR (MIR)
spectroscopy.
Penetration
Depth
The
depth of penetration is defined by the formula:
where
l
is
the wavelength of the infrared light, n_{1}
is the refractive index of the ATR crystal,
is the angle of incidence of the infrared beam at
the boundary and n_{21}
is the ratio of the refractive indices of the sample,
n_{s} and ATR crystal,
Since the evanescent wave decreases in intensity
exponentially from the surface of the crystal, the
penetration depth, d_{p}, is defined as
the distance at which the amplitude of this wave
has decreased to (1/e) or 37% of its original value.
Effective
Angle of Incidence
This
is the angle of incidence of the infrared beam internally
in the ATR crystal when a variable angle HATR such
as the Varimax™ is used for analysis. When
the scale angle, _{scale},
is not equal to the crystal face angle, _{face},
the effective angle,
is different than the scale angle due to refraction.
Number
of Reflections
The
number of reflections in the crystal gives a measure
of the intensity of the resulting spectrum. This
number is a function of the effective angle of incidence
, and
the length, I, and thickness, t, of the crystal.
Effective
Pathlength
The
effective pathlength, P_{eff}, is defined
as the product of the penetration depth d_{p},
and the number of bounces, N, the IR beam makes
within the crystal:
