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 ...!{akgua,allegra,amd,hplabs,ihnp4,masscomp,ut-ngp}!gatech!gtss!chas ...!{rlgvax,sb1,uf-cgrl,unmvax,ut-sally}!gatech!gtss!chas