Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site gtss.UUCP Path: utzoo!watmath!clyde!bonnie!akgua!gatech!gtss!chas From: chas@gtss.UUCP (Charles Cleveland) Newsgroups: net.physics Subject: Re: Real Physics -- Specific Heat of Glasses Message-ID: <112@gtss.UUCP> Date: Fri, 17-May-85 11:39:37 EDT Article-I.D.: gtss.112 Posted: Fri May 17 11:39:37 1985 Date-Received: Sat, 18-May-85 02:22:21 EDT References: <1397@mtx5b.UUCP> <> <713@oddjob.UUCP> Reply-To: chas@gtss.UUCP (Charles Cleveland) Organization: Georgia Tech Surface Studies Lines: 79 Keywords: specific heat, metals, glasses Summary: 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 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