﻿342 
  Fenner 
  — 
  Stability 
  Relations 
  of 
  Silica 
  Minerals. 
  

  

  explained 
  by 
  the 
  assumption 
  of 
  two 
  different 
  kinds 
  of 
  molecules 
  

   in 
  the 
  same 
  crystals. 
  It 
  seems 
  most 
  probable, 
  therefore, 
  in 
  con- 
  

   sideration 
  of 
  all 
  the 
  phenomena, 
  that 
  different 
  molecular 
  group- 
  

   ings 
  of 
  Si0 
  2 
  take 
  place 
  in 
  the 
  melt 
  under 
  the 
  circumstances 
  

   described, 
  and 
  that 
  when 
  crystallization 
  ensues, 
  these 
  complex 
  

   molecules 
  arrange 
  themselves 
  in 
  the 
  appropriate 
  patterns 
  

   corresponding 
  to 
  the 
  respective 
  crystals. 
  The 
  minerals 
  are 
  

   regarded, 
  therefore, 
  as 
  being 
  not 
  only 
  polymorphic 
  but 
  poly- 
  

   meric. 
  

  

  The 
  reactions 
  of 
  silica 
  which 
  have 
  been 
  mentioned 
  appear 
  

   to 
  follow 
  very 
  closely 
  the 
  requirements 
  of 
  the 
  principle 
  which 
  

   Ostwald 
  enunciated 
  and 
  which 
  is 
  known 
  as 
  Ostwald's 
  rule, 
  or 
  

   the 
  law 
  of 
  successive 
  reactions. 
  As 
  formulated 
  by 
  him, 
  it 
  is 
  

   as 
  follows 
  :* 
  u 
  In 
  all 
  reactions 
  the 
  most 
  stable 
  state 
  is 
  not 
  

   straightway 
  reached, 
  but 
  the 
  next 
  less 
  stable 
  or 
  that 
  state 
  

   which 
  is 
  the 
  least 
  stable 
  of 
  the 
  possible 
  states." 
  The 
  reason- 
  

   ing 
  by 
  which 
  he 
  endeavors 
  to 
  show 
  the 
  necessity 
  of 
  reactions 
  

   taking 
  this 
  course 
  is 
  based 
  upon 
  a 
  consideration 
  of 
  the 
  diminu- 
  

   tion 
  of 
  free 
  energy 
  of 
  a 
  system. 
  It 
  seems 
  to 
  imply 
  that 
  

   because 
  the 
  free 
  energy 
  in 
  passing 
  from 
  a 
  stage 
  A 
  to 
  a 
  lower 
  

   stage 
  C 
  passes 
  through 
  the 
  level 
  B, 
  the 
  phase 
  corresponding 
  

   to 
  this 
  level 
  must 
  always 
  appear, 
  but 
  there 
  is 
  no 
  necessity 
  that 
  

   this 
  should 
  hold. 
  The 
  matter 
  resolves 
  itself 
  into 
  the 
  question 
  

   whether 
  under 
  unstable 
  conditions 
  the 
  quantity 
  of 
  free 
  energy 
  

   in 
  a 
  system 
  defines 
  its 
  state. 
  Expressed 
  in 
  this 
  form, 
  we 
  can 
  

   answer 
  definitely 
  that 
  it 
  does 
  not, 
  any 
  more 
  than 
  the 
  somewhat 
  

   parallel 
  functions 
  of 
  vapor-pressure 
  or 
  thermodynamic 
  poten- 
  

   tial. 
  

  

  Applying 
  a 
  kinetic 
  conception, 
  if 
  we 
  can 
  imagine 
  a 
  sodic 
  

   tungstate 
  melt 
  saturated 
  with 
  simple 
  ungrouped 
  silica 
  mole- 
  

   cules 
  at 
  850°, 
  and 
  then 
  allow 
  such 
  reactions 
  as 
  tend 
  toward 
  

   equilibrium 
  to 
  take 
  place 
  for 
  a 
  minute 
  space 
  of 
  time, 
  while 
  it 
  

   is 
  probable 
  that 
  cristobalite 
  groups, 
  because 
  of 
  the 
  relative 
  

   simplicity 
  of 
  structure 
  usually 
  accompanying 
  high 
  temperature 
  

   forms, 
  will 
  have 
  been 
  produced 
  in 
  greater 
  numbers 
  than 
  tri- 
  

   dymite 
  groups, 
  yet 
  at 
  the 
  end 
  of 
  a 
  longer 
  interval 
  it 
  is 
  doubt- 
  

   ful 
  if 
  this 
  would 
  be 
  the 
  case. 
  The 
  strength 
  of 
  the 
  union 
  

   holding 
  together 
  the 
  members 
  of 
  each 
  cristobalite 
  group 
  would 
  

   probably 
  be 
  so 
  slight 
  at 
  this 
  temperature 
  that 
  after 
  the 
  rapid 
  

   attainment 
  of 
  a 
  certain 
  maximum 
  number, 
  equivalent 
  numbers 
  

   would 
  be 
  destroyed 
  as 
  rapidly 
  as 
  others 
  formed, 
  while 
  the 
  

   number 
  of 
  tridymite 
  groups 
  would 
  continually 
  increase 
  until 
  

   the 
  solvent 
  was 
  saturated 
  and 
  crystals 
  were 
  deposited. 
  In 
  the 
  

   latter 
  sequence 
  of 
  events, 
  the 
  level 
  of 
  free 
  energy 
  represented 
  

   by 
  B 
  would 
  be 
  that 
  pertaining 
  to 
  a 
  mixture 
  composed 
  mostly 
  

  

  * 
  W. 
  Ostwald, 
  Principles 
  of 
  Inorganic 
  Chemistry 
  ; 
  translation 
  by 
  A. 
  Find- 
  

   lay, 
  1904, 
  p. 
  211. 
  

  

  