[net.physics] Real Physics -- Specific Heat of Glasses

sra@oddjob.UUCP (Scott R. Anderson) (05/11/85)

In article <1397@mtx5b.UUCP> mat@mtx5b.UUCP (Mark Terribile) writes:

>The specific heat of metals is very low ... approximately one fifth to
>one tenth that of water.  Ceramics and glassy materials have specific
>heats that are approximately the specific heat of water, give or take
>a factor of one part in three.
>	Is the specific heat of <a metallic glass> more reminiscent of the
>specific heat of the metallic phase of the material, or is it reminiscent
>of the specific heat of glass?

In article <> chas@gtss.UUCP (Charles Cleveland) writes:

>If you examine specific heats in some reasonable units (such as calories
>per degree kelvin per atom) you will find that there is no systematic
>variation is specific heats as one moves between materials belonging
>to the classes you consider...The variations do not particularly have
>to do with crystalline vs. amorphous or insulator vs. conductor.  These
>are about room temperature considerations (specific heat dominated by
>'lattice vibrations'.

    It should be pointed out that there is more than one kind of specific
heat:  Cv, the specific heat measured at constant volume, and Cp, the
specific heat measured at constant pressure.  What Charles refers to is
Cv, which is relatively constant amongst solids at room temperature.
However, it is much easier to measure Cp, so that is usually what is
reported in handbooks of materials.  I believe this is what Mark refers
to.  The difference between the two is an equation of thermodynamics
which involves the adiabatic and isothermal compressibilities of the
material.
    Cp for water is 1 cal/g-K (this is the definition of the calorie)
or 18 cal/mol-K, while most metals are about 5 cal/mol-K.  "Ordinary"
glasses are indeed around 20 cal/mol-K, but this is about half of the
specific heat of the corresponding liquid phase; the specific heat of
the glass phase is only slightly higher than that of the crystalline
phase.  The latter is also true of metallic glasses; i.e., the answer
to Mark's question is 'yes' (:-).

					Scott Anderson
					ihnp4!oddjob!kaos!sra

chas@gtss.UUCP (Charles Cleveland) (05/17/85)

In article <713@oddjob.UUCP> sra@oddjob.UUCP (Scott R. Anderson) writes:
>In article <1397@mtx5b.UUCP> mat@mtx5b.UUCP (Mark Terribile) writes:
>
>>The specific heat of metals is very low ... approximately one fifth to
>>one tenth that of water.  Ceramics and glassy materials have specific
>>heats that are approximately the specific heat of water, give or take
>>a factor of one part in three.
>>	Is the specific heat of <a metallic glass> more reminiscent of the
>>specific heat of the metallic phase of the material, or is it reminiscent
>>of the specific heat of glass?
>
>In article <> chas@gtss.UUCP (Charles Cleveland) writes:
>
>>If you examine specific heats in some reasonable units (such as calories
>>per degree kelvin per atom) you will find that there is no systematic
>>variation is specific heats as one moves between materials belonging
>>to the classes you consider...The variations do not particularly have
>>to do with crystalline vs. amorphous or insulator vs. conductor.  These
>>are about room temperature considerations (specific heat dominated by
>>'lattice vibrations'.
>
>    It should be pointed out that there is more than one kind of specific
>heat:  Cv, the specific heat measured at constant volume, and Cp, the
>specific heat measured at constant pressure.  What Charles refers to is
>Cv, which is relatively constant amongst solids at room temperature.
>However, it is much easier to measure Cp, so that is usually what is
>reported in handbooks of materials.  I believe this is what Mark refers
>to.  The difference between the two is an equation of thermodynamics
>which involves the adiabatic and isothermal compressibilities of the
>material.
>    Cp for water is 1 cal/g-K (this is the definition of the calorie)
>or 18 cal/mol-K, while most metals are about 5 cal/mol-K.  "Ordinary"
>glasses are indeed around 20 cal/mol-K, but this is about half of the
>specific heat of the corresponding liquid phase; the specific heat of
>the glass phase is only slightly higher than that of the crystalline
>phase.  The latter is also true of metallic glasses; i.e., the answer
>to Mark's question is 'yes' (:-).
>
>					Scott Anderson
>					ihnp4!oddjob!kaos!sra

	Let's beat this old horse a little more.  To quote Kittel,"For
solids the difference between Cv and Cp is usually small and often may be
neglected, particularly below room temperature." In fact, however, the values
I looked up before I wrote my previous response were Cp's.  The terminally
astute reader (:-) of the above will have noticed that I chose cal/atom-K as
my unit and not cal/mol-K.  Thus to convert Scott's numbers to my units,
apart from an overall factor of Avogadro's number, divide Cp(H2O) by 3 and
since ordinary glasses are mostly SiO2 divide Cp(ordinary glasses) by 3 too.
	The few exceptions generally arise when a material is very 'stiff',
so that it supports very high vibrational frequencies which are not 'fully'
populated at room temperature--this situation is reflected in a high Debye
temperature.  See diamond vs. graphite below.
	For the possible amusement of anyone still reading this here is
a brief table:

material	Cp [cal/atom-K] x Avog. #	Debye temperature [deg K]

Ni			5.9				 450
Na			6.72				 158
H2O			6				  ?
Si			4.8				 640
Zn			6.1				 327
(ord. glass)		6.6				  ?
I2			6.5				 106
Be			3.93				1440
C(graphite)		6.26				 420
C(diamond)		2.04				2230

	Note that Cp varies much less than the Debye temperature and that
of the materials listed only diamond and to a lesser extent beryllium fall
much outside the range of say, 5-7.
	In short, the answer is still yes.
-- 
Charles Cleveland			 Georgia Tech Surface Studies
Georgia Tech School of Physics
Atlanta, GA 30332
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